Question

If a fossilized Pokemon in X/Y is level 20, will it learn all remember all it's move until that level?

Answer 1

Yes, a lv. 20 Fossil Pokémon will learn all the moves it can up to that level (but only four of course). For example, a newly-revived Amaura will know Aurora Beam, Mist, Icy Wind and Take Down.

Source: Experience