If I have a Memory Energy attached to an Incineroar that evolved from a Litten with the "Caturday" attack, with Persian's "Gathering of Cats" Ability are all my Incineroar's attacks now free?
No, it doesn't work like that. Memory Energy lets you USE attacks from its previous Evolutions, but it doesn't GIVE it those attacks. Therefore, Gathering of Cats would have no effect on the Incineroar.
Gathering of CatsMemory Energy