This was Theme Week Bugs.

What two kinds of insect are associated with Buzz Buzz over the course of the game, in dialogue or otherwise? Bees and bung deetles. Uh, dung beetles.
Say that you proceed through the game, that you acquire the melodies in order, and that you acquire Magnet Hill as soon as you're contacted by Mr. Spoon. What's the last enemy (that looks like an insect) that you gain the opportunity to fight? (Note: neither spiders nor slugs are insects for the purposes of this question.) The Filthy Attack Roach (in the Fourside sewers) or the Master Criminal Worm (although its name isn't "insectoid", it does resemble the Criminal Caterpillar, which is an insect).
Which insect has the most enemies (including one boss) based on it? With 4 enemies (including the boss), the ant.
Aside from the boss, name two of the enemies referred to in question 3. The Black and Red Antoids, and the Gigantic Ant. (The Titanic Ant is the boss.)
What rare, 1/128 item affects only insect enemies? XTerminator Spray.

This week, we saw 100% correct answers given by Artemis251, Asanyne, Banana, Black Mage of Pain, bluegoo26, bowser, bstring, Captain JonJovi, Culix, Foppy King, Gauntlet, Giegue, GreenCat, JaydeWizard, Jeff of Dalaam, Jeff's Radio, Kahran042, LeChimp, Libra, LordBob Bree, Master JSP, Meridith_Richtore, nekoaitsu, Nearsighted Orange, Ninten1, Pharon, Ravenshaw, Revival of Buzz Buzz, Salookanana, SimonBob, Skeletor, SkyeChan, SneakyLlama, STAREYe, Strawberry Tofu, SuperStarman Deluxe, Tails98, Treasure, Vi, WhoopA, and Zasheir.

This was Theme Week Extreme.

In general, which of the four main characters will have the most PP if they all reach level 99 while robots? (Assume that IQ capsules and IQ raises by the Rock candy trick have not disproportionately benefited a character.) This would be Ness, as he goes from 5 PP/IQ to 15 PP/IQ at the end of Magicant. (Which means that unless Paula or Poo's IQs more than treble his IQ by the time they reach level 99, he has more than they do.)
If you fight one of each enemy that you can on your way to pick up Picky from the meteorite site, what item are you most likely to find in a present after a battle? The Cookie, as Crows leave it persistently.
When you attempt to leave the Fourside Mall for the first time after going to a higher floor, in whose inventory would it be most unintelligent to have placed the Franklin badge? Paula, as she gets kidnapped and then you have to run a Musica gauntlet without it.
Which item repairable by Jeff can reduce the HP of the most enemies? The Broken tube or the Hungry HP-sucker. It will suck HP from every on-screen enemy, reducing their HP but not damaging them.
On the other hand, which item repairable by Jeff can deal damage to the greatest number of enemies? (Note: 4 and 5 have different answers; the italicised portions are big hints.) The Broken bazooka, which is mended to the Heavy bazooka. It operates like an infinite Super bomb, damaging not only the target enemy, but some of the enemies on the same row. (The rest of Jeff's repairable items either don't affect enemies, like the Defense shower; affect enemies but don't deal damage, like the Slime generator and Shield killer; or are equippable weapons that damage a single enemy, like all the Beams he repairs.

Congratulate: Ambi, Archon Divinus, Artemis251, Asanyne, Black Mage of Pain, bowser, bstring, David Shelton, DDR Paladin, dubs, EB Master, Foppy King, Giegue, gigadragoon89, Greenflannel, Highwayman Johnny, InLikeFlint, JeffMan, Jeff's Radio, jmike, leth, Libra, Master JSP, nb2k, Nearsighted Orange, Pedro, Plarplethingie, Psychic Kid, Radiation, Ravenshaw, Salookanana, Scott Dumblauskas, shamansanchez, SimonBob, SkyCroc, Starman Omega, steveman0, Tails98, Wyborn, Zach.

This was the very experimental Jeopardy! week.

Crossword Clues "G": The first name of a prominent Foursidian (10). (You must have the exact spelling. The answer begins with G.) What is Geldegarde? (I didn't accept "Geldegarde Monotoli", as that is not his first name.)
Rhyme Time (e.g. "The tie of a spiteful Onett enemy" = "Crow bow"): The gold mine in Dusty Dunes Desert to the Guardian Diggers and/or the guardian of Lilliput Steps, perhaps? (Hint: the two words in this response are spelled with the same number of letters.) What is a mole hole?
Before and After (e.g. "Princess Peach's realm of green spore-scattering enemies" = "Struttin' Evil Mushroom Kingdom"): Your Sanctuary weapon that can be acquired from the Deep Darkness Tenda Village's trading post. What is the Lumine Hall of fame bat?
Eagleland Politics: The only person who is explicitly said to hold an elected position in Eagleland. Who is (Mayor) (B.H.) Pirkle?
Stupid Answers: This foreign enemy might give the kiss of death, but maybe it's all in your mind. What is the French Kiss of Death? And yes, I did add that last qualification to avoid people answering "Kiss of Death".

Final Jeopardy
Gigantic Lists of Names: These people won the Jeopardy! theme week.
Who are BlackMageOfPain, TheBlueAvenger, bluegoo26, bstring, DJ Gear, ebunleashed, Fourside Resident, Gauntlet, Goggles, GreenCat, Kahran042, kidbond, K Rob, LeChimp, leth, LordBobBree, Moochie, Sarahsuke, SuperStarmanDeluxe, Waitohooru, WhoopA, and WolFox?

The theme this week was Feminine Wiles.

What three attack PSI (that is, PSI that deal HP damage) have appeared in all three Mother games? (Hint: keep this week's theme in mind and it'll come to you easily.) Fire, Freeze and Thunder. (Come on, the theme was female-centric, which should've hinted heavily that Paula used those PSI.)
What two ribbons are the rarest, not because they're 1/128 items, but because there's only one of each of them in the entire game? The Saturn and Talisman ribbons.
What item held by Paula when you free her from the cabin in Peaceful Rest Valley might help her survive some early battles by drawing attacks away from her? The Teddy bear.
What six-letter word best describes the disposition of the only female human enemies in EarthBound? Cranky.
Mothers aside, who are the first two female characters it's necessary to speak with in order to progress through the game? Paula and the Runaway Five fan in the songroom at the Chaos Theatre. Alternately, I accepted the ticket lady there - technically, all you do with her is present your Backstage Pass, but some people might construe that as speaking with her.

Predominantly if not entirely male, these people got in touch with their feminine sides: brocoli, Cannotthink, Cyan683, Gennenalyse Rueben, JeffMan, leth, Master JSP, Ninten1, Podo, Salookanana, WhoopA.

Theme Week Luck. Were you willing to bet your life?

Despite the lore associated with its real-world form, what item equipped on the body does not affect Luck at all? The item I had in mind was the Rabbit's foot. I also accepted the various Charms; as the Lucky coin is equipped as "Other", I didn't count it.
Who are two of the people associated with the slot machine, the only part of the game (optional as it is) where luck (not Luck) really applies? (If you give family relations, give names as well.) Pincho, Pancho and Tomas Jefferson. (No, Radiation, I didn't count the one Chick you can win.)
What are two items whose loss (either because it was used or because it was removed from your inventory/inventories through an event) might/will result in an increase in a character's Luck? (Ignore increases through level-ups.) The Rock candy may increase Luck, the Luck capsule will, and the loss of the Sound stone after Magicant will.
With which bat will Ness have been luckiest to hit an enemy 16 consecutive times? (Assuming the enemy has the HP to survive 16 rounds of battles, including however many SMAAASH attacks there are in those 16 rounds.) The Casey bat, which has the lowest accuracy, by far, of the various bats Ness can equip.
What two single-use, edible items (in both cases notwithstanding the use of the ...condiment trick) have multiple effects, meaning whatever effect they have is dependent on luck? The Rock candy (increases a random stat by 1) and the Lucky sandwich. Also, the Secret herb, if used on an unconscious character (it may not work).

The luckiest people were Adrian Cornwall, Archon Divinus, brocoli, chuggaaconroy, CodPor, Cyan683, darklink570, Dr. Baconman, Gennenanlyse Rueben, Goggles, Kahran042, kidbond, kota12, leth, The Losar, MasterJSP, Radiation, SimonBob, Tails98, Tobias26, TonySaturn, WhoopA and Zach.

Jeopardy! Theme Week #2.

Before and After (e.g. Your Sanctuary guardian pretending to be a minor enemy in his dungeon: 'Mondo Mole Playing Rough'): This PSI/PK attack causes a Your Sanctuary to erupt from the caster's fingers. What is PSI Fire Spring?
Rhyme Time (the answer rhymes): Command given to Ness' dog to get him to perform Yellow Submarine or Hey Jude. (Note: two syllables long.) What are either "Sing, King!" or "King, sing!"?
A Girl's Best Friend: Hello, I'm Marilyn Monroe/Carol Channing/Nicole Kidman). This arm equipment is the only (actually one of two) equippable item in EarthBound that can be purchased at two different prices. (VERY BIG HINT: this title refers to a song that all three actors named above sang at one point or another.) What is the Diamond band?
OMG "Ban" From Chan (answer will contain "ban"): This item for barter is both regal as well as a berry (so they say). What is the King Banana?
Common Bonds: Starman, Yes Man, and perhaps an unseen Mook. What are (or might be) Juniors? (Starman Junior, Yes Man Junior, and although we never see it, a Mook Junior, since there is a Mook Senior.)

Archon Divinus, TheBlueAvenger, Bluegoo 26, Daniel, Gauntlet, GreenCat, Kahran042, Kelli, leth, Libra, Moochie, Tails98, toader, Tonto Goldstein, WhoopA returned to defend their titles next week.

This was Theme Week Shrubberies.

What two buildings must you enter in order to acquire an item that will recover one character's PP by trading for that item? First the Threed Hospital, to get the Insignificant item, then the Twoson Hospital, to trade that item for the Magic truffle.
Ignoring the residents of the Monkey Cave, who are two of the three people it's necessary to give food Ness and his friends can eat (so neither the Yogurt dispenser nor Tendakraut count) to in order to progress in the game? (Yes, I know they eat Trout yogurt, but that's not the dispenser.) Apple Kid; Gerardo Montague, the miner; the scruffy boy near Jackie's Café; and the Bubble Monkey (arguably).
What's the reward Ness gets for returning a memento that was lost in Dusty Dunes by a resident of Fourside? A pair of dirty socks.
What formerly edible item has to be brought to another resident of Fourside in order to access the sewers? A (signed) banana (peel).
What are two of the three items you can receive from the Deep Darkness Tenda Chief after having brought him the Shyness book? Tendakraut, Bag of Dragonite, the Shyness book.

BlackMageofPain, Bluegoo26, bstring, Culix, David Shelton, Dr. Ancookie, Dr. Baconman, EB Master, Gauntlet, Goggles, Incoherent_Moron, JeffMan, Kahran042, Kelli, kota12, leth, Lord Bob Bree, The Losar, Mad William Vane, Nearsighted Orange, Pharon, PK Boo, Ravenshaw, shivndragon, SimonBob, Tails98 and WhoopA all won this time around.

This was Theme Week Pokey. Or Porky for the Mother 2 purists among us.

What are the two locations in the game that are themselves listed as Teleport locations (i.e., not that one cave in the Lost Underworld from which you travel to the past) where Pokey left something that you can see outside dialogue that indicates he was there (even though he's not there when you're in those locations)? He left Monotoli's wrecked helicopter in Deep Darkness, and ... um, his droppings in Scaraba.
Are physical attacks all that Pokey can do in the final battle? No, he can expel stinky gases (which aren't physical), and also do things like talk smack to you (courtesy JeffMan).
With which two people known to have been in possession of the Mani Mani Statue was Pokey never seen to associate? Lier X. Agerate unearthed the Mani Mani Statue and sold it to Carpainter, from whom Everdred stole it.
Just where did Pokey leave graffiti on billboards (which generally served to insult Ness)? Summers. Or Toto. I wasn't particular.
What epithet is used for Pokey during the coffee/tea scenes? Worst person in the neighbourhood.

Dr. Baconman, bluegoo26, chuggaaconroy, CodPor, Culix, Elnendil, Fred, JeffMan, MasterJSP, SutterCane, Tails98, WhoopA, and zztman won this week.

This was a theme week for the boys in blue.

Why does Captain Strong feel he has to resort to using his Super Ultra Mambo Tango Foxtrot martial arts when he fights you? He feels he'd lose in a fair fight.
What's the only city in the game shown to have police but no police enemies (either boss or free-encounter)? Fourside. Cities that have police enemies are Onett, Twoson and Summers (though not all have police).
How does the cop that confronts you as you're leaving Giant Step after acquiring its melody describe Ness if you answer "No" to his question? Rebellious youth, roughly.
What part of policing does the only policewoman in the game expect to go into later on in the game? Parking enforcement. Yes, Mr. Itoi, S. Terry Otype is on Line 2. (Alternately, address this statement Dan Owsen or whoever localised the dialogue.)
What two enemies are most commonly found joining in with police-type enemies in battle? Runaway Dogs and Tough Guys.

Dr. Baconman, bluegoo26, CodPor, Culix, Goggles, JeffMan, Matt, SilverStreak and Tails98 won this time around.

A theme week on the Franklin badge. Are you shocked surprised?

Against which two Your Sanctuary guardians might the Franklin badge actually be useful? Thunder and Storm and Electro Specter are the two guardians in question.
What "first" (in terms of your party) do the character who gives Ninten the Franklin badge in Mother 1 and the character who gives Ness the Franklin badge in EarthBound both achieve? Pippi and Paula are the first female/controllable/experience-earning characters to join the party. (You had to get one of those points across, as Pokey, Picky, Buzz Buzz and optionally King all join your party before Paula does.)
What's the first non-boss enemy you can encounter against which the Franklin badge would be a help? Believe it or not, the Skelpion.
In EarthBound (and not necessarily the other games), what are two attacks (PSI and/or otherwise) that the Franklin badge will reflect? (Yes, I mean something like "glorious light" or "mysterious electric field", not "electricity-based attacks".) First you encounter Crashing Boom Bang attacks, then PSI Thunder, then electrical shock attacks. Oh, and a particular type of Giygas' incomprehensible attacks.
If you speak with Carpainter before obtaining the Franklin badge, which Happy Happy Village resident will joke about Carpainter moving you if you talk to her? The cow.

Tails98 was the only person to win this week around.