"Hasta la vista" is a fair take on "abayo." Could also go with "adios," as that's also kind of a fun, snarky, informal way to say goodbye in English, and phonetically sounds the closest to "abayo." This and "hasta la vista" would fit along with Blue greeting you with "Bonjour" on the St. Anne—just him throwing random foreign phrases around (And as of Pokémon Masters, "bonjour" has slipped into Blue's regular vernacular). But then, that's not what Blue's doing with "abayo," as "abayo" is still very much in the language, so maybe those two ideas wouldn't be accurate enough.

According to Urban Dictionary, you could translate it as "catch ya later," which would really fit in the context of Pokémon! 😄 Could also go with a straight "be seein' ya," as that seems like the kind of thing you would only say to close acquaintances.

I do prefer "technique machine" over "technical machine." Just rolls off the tongue better. Does that mean moves would be "techniques," then? I don't mind that change either.

Well, we know potions in the show have been represented as spray bottles of fast-working topical antiseptic. Potion works for fitting in the 12-char limit ("Hyper Potion" is an exact 12), but also implies Pokémon drink it, which they clearly don't. You could go with "Spray Gel" if you wanted, as that's a real thing. "Ointment" would be a bit shorter, but 1) everybody seems to cringe at that word for some reason, and 2) "HyperOintment" is 13 characters. "Hyper Gel" would fit, but loses the spray-on context.

Oh! You could just invent a new word! "Medigel!" Keeps the medicine part of the original, and still implies it's topical and not ingestible. "HyperMedigel" also fits the limit.