if a pet doesn't have a skill, let's say spritely, on its 10 talents list can it still get spritely? I particularly want a brainy assistant that knows spritely or the may cast unicorn skill
Pets that you buy or get as quest rewards or drops in game (first generation) have a set talent list, and can only get up to 5/10 of those possible talents.
Hatched pets inherit talents from parents, so it is possible to make any pet that can be hatched with any combination of talents, though it may take quite a few hatches to get an exact set.
Jewels can add a talent that you select to any pet, independent of starting gene pool/
if a pet doesn't have a skill, let's say spritely, on its 10 talents list can it still get spritely? I particularly want a brainy assistant that knows spritely or the may cast unicorn skill
Spritely is not in a first generation Brainy Assistant's talent pool so you will not get it. The only way to get it is to hatch with another pet that either already has it or at least has the potential to learn it.