Firechu is mixed Electric/Fire and will know Blast Burn when caught.
Grasschu is mixed Electric/Grass and will know Frenzy Plant when caught.
Waterchu is mixed Electric/Water and will know Hydro Cannon when caught.
They can't learn any other moves that aren't in normal Pichu/Pikachu/Raichu's movepools.
Important! The Pokémon will only know these moves when caught in the wild. The ones hatched from eggs will not have the extra moves. They will still have the mixed types, however. If you adopt a Pokémon from Gacha, it will still know the moves if it knew them when it was released.
You have a 1 in 500 chance of finding them in the map and they have a 1 in 3 chance of being shiny (so 1/750 chance of normal and 1/1500 chance of shiny).
All Typechu can't be found in water routes or fishing, and otherwise have no restrictions to appear (so yes they can appear in Mirage Island, while refreshing for events, et cetera).
Just to reiterate, Odor Sleuth and the Fluffy Tail don't work on them. Other items like Mean Look work normally.
They can be Everstone bred at a 2% success rate when you own an Egg Scope (1% otherwise). Each Pokémon's sprite type is different, so you can only breed a Firechu from a Firechu and so forth.
Shiny Typechu can be used to breed with BrightPowder.
You can use Plain Incense to breed Pikachu rather than Pichu.
They're normal Pichu/Pikachu/Raichu in every other aspect including evolution method, catch rate, experience curve, base Daycare fee, et cetera.