I have a question,

After using role play, when the battle ends, it is suposed to keep the ability of the other pokemon?

no, it will change back if you heal it at nurse joy.

i'm using sync to search for a Swift Swim poliwag, after using role play, my abra either keep sync ability or change to damp/ water absorb, so i don't if is some kind of bug when, after the battle, it kept damp or water absorb or when it come back to sync, even before healing at pokecenter

102349 i'm using sync to search for a Swift Swim poliwag, after using role play, my abra either keep sync ability or change to damp/ water absorb, so i don't if is some kind of bug when, after the battle, it kept damp or water absorb or when it come back to sync, even before healing at pokecenter

interact with nurse joy again or lay them down at the pc after doing that. it should fix the ability

Does copied ability works normaly if you dont go heal at pokecenter? people could abuse this

102434 Does copied ability works normaly if you dont go heal at pokecenter? people could abuse this

it still should be the same ability as before. however, healing the pokemon via nurse joy will "heal" the ability aswell.