1.Stats: Should Relicanth get a stat boost, Evolution, Mega Evolution or nothing?
Relicanth can get +55 BST, but +10 or +40 BST would be sufficient enough to match other fossilmons.
Relicanth would enjoy an Evolution over a Mega, but a pre-evo would be better.
2.Should Relicanth get more abilities?
Regenerator could be cool, so can Water Veil.
3. Should Relicanth get more moves?
Generally yes. Relicanth has been getting a few moves recently, but none of them were particularly good.
4.What additional typing Relicanth can have?
Ground, Psychic, Ice are options. Fighting, Flying and Normal are lesser options.