1.Stats: Should Medicham get a stat boost, Evolution, Mega Evolution or nothing?
Medicham can get +10 BST to match Azumarill.
An Evolution would be better, but it is a bit impossible with Mega Medicham. Maybe another third stage can occur as a pre-evo for Meditite or mid-evo.
Another Mega Evolution focusing on Special Attack would be badass.
2.Should Medicham get more abilities?
Probably. Prankster seems a decent Ability. Dancer can also work. Something smaller like Iron Fist and Reckless can also work.
3.Should Medicham get more moves?
Meteor Mash is an option. More seriously, Sky Uppercut and Blaze Kick are pretty necessary. So is Zen Headbutt for Meditite(Medicham already gets it).
4.What additional typing Medicham can have?
Ghost is the most obvious one. Elemental types and Dark can also work.