1.Stats: Should Persian get a stat boost, Evolution, Mega Evolution or nothing?
Persian can get +15 BST to match Primeape, and at maximum can get +100 BST.
Both forms would enjoy an evolution.
A Mega without Fur Coat for both would be a waste.
2.Should Persian get more abilities?
Speed Boost and Prankster are options. Pickpocket is another option.
3.Should Persian get more moves?
Swords Dance would be nice.
4.What additional typing Persian can have?
Dark and Normal variants already exist, so Electric and Fairy are options.