Galaxy Expedition.

I just wanted to point out, you got Dyson Spheres effect mixed around.

And uhm.. Mini Guts is good for Chronomalies Number 33: OOPArts Super Weapon Machu Mach.  It's good because it reduces a monsters ATK to 0 which combos with Machu Mach, it inflicts effect damage from 33, it boosts 33's ATK via its own effect, and then attack with 33 inflict battle damage and then more damage from mini guts effect.

Mmmm gimmick puppets is difficult.. Gearspring Spirit is good because it is a level 8 monster with an easy summoning condition, and it can reduce a monster ATK to 0.

For V's Deck... He plays a space themed deck (new cards shown in his tag duel with Kaito.). And Tannhäuser Gate is a good card to use for Sky Canopy Star, because Tannhäuser targets 2 monsters and makes their levels the sum of their combined levels.

Heraldics... I really don't know because Konami botched their boss monsters effect.. So I guess like.. Lavaval Chain.. Because it can send a monster from the deck to the grave... And most heraldics get their effect from the graveyard.

Chronomaly: Honest. A lot of the Chronomaly monsters are Lights so they would really benefit from this card.

Gimmick Puppets: Gearspring Spirit is really good in this deck, it adds a lot of speed which helps bring out rank 8s faster.

Number 9: Uh... Xyz Reborn I guess? Bring back Dyson Sphere, then when it gets attacked, attach 2 more materials to it.

Heraldics: 2 ideas for this one. Return from the Different Dimension, which specials all the monsters which have been banished for their effects, so you can spam xyzs. Also Burial from a Different Dimension to return your monsters to the grave so you can banish them for their effects again.

Bad lesson is bad. I thought lessons was about teaching people about the game in general, not specific decks that have no relevance at all. Not even mentioning that the number of answers is quite restricted.

Chronomaly: As you said, Chaos plays can be made, and when it comes to Chaos nothing goes over BLS. Mini-Guts has already been explained and it probably is the best tech card for Chronomalys.

Gimmick Puppets: Inferno Reckless Summon. Although Gimmick Puppets are a high rank/level archtype, they mostly have low attacks and Special Summon themselfs/others making Inferno a perfect card to spam them and instantly make the big rank 8s.

Number 9: Photon Satellite. We all know that Photon/Galaxy can spam out level/rank 8s, combining those with Satellite you get level 9s and therefore the perfect material for Dyson Sphere. Galaxy/Photon is the only deck I could thing off that is able to easily get out Dyson Sphere and it does fit its space theme.

Heraldics: Summoner Monk. You run a lot of Spells and Monk gives the speed it needs in the early game. The possibility of instantly going into Lavaval Chain to get your effects going is awesome.

Chronomally: birdman, the machu mech otk is a boring build :p the 3,5,8 build is way faster. Since chronomalys can ss themselves u can just bounce em back for a birdman (like geargiaccel) 
Gimick puppets:trade in, if ur running only the lvl 8 cards the deck won't start moving unless u can dump a monster
Dyson sphere: lemuria, the forgotten city, iv'e gotten double dyson spheres out ez with this deck. All u need rly is the ancient deep sea king or nimble's.
Heraldics: chain dog, dire wolf loop iz ez to pull here n chain dog can spam A LOT in heraldics.

III/Trey/Chronomalies: I'd say Machu Mech + Genom-Heritage. Drain a pesky Xyz with Genom, then smack 'em in the face with Machu.

IV/Quatro/Gimmick Puppets: Galaxy Queen's Light in case you cant Xyz yet while you hold a Level 8 on your field. Hits all your other monster's Levels, straight to an equal level of your 7+s.

V/Quinton/Dyson Sphere: Battle Mania if you need more Materials before something big appears on the field to knock #9 out of orbit. Use it while there are weaker monsters than Dyson Sphere only on the field, or you'll end up in orbit with it.

Tron/Vetrix/Heraldic Beasts: If you steal the powers/Materials of a useful, 2 Mat. Cost effect, Genom would be close to using it twice, OR, steal more units if you want to keep your opp's Xyz down/keep this stealing Psychic going. Overlay Regen can be helpful in making that second use happen, or keep the sneaky thing snatchin' more Mats.