1.Stats: Should Exeggutor get a stat boost, Evolution, Mega Evolution or nothing?
+10 BST is most Exeggutor can get.
A middle evolution would be more fitting if it wasn't a stone Evolution.
A Mega would be very fitting, but most focus on Speed.
2.Should Exeggutor get more abilities?
Yes. Leaf Guard, Grassy Surge, Synchronize, Psychic Terrain and other stuff are options.
3.Should Exeggutor get more moves?
Stored Power is an option. Dragon Dance is another for Alolan Variant.
4.What additional typing Exeggutor can have?
Normal, Poison and Fire are options. Ground is another.