{Inkmoth Nexus} - if someone turns it into the 1/1 and I kill it with {Gruul Charm} (3 Dmg to target creature w/ flying) does it go to the graveyard?
Yep just like it was an actual creature. Unless they give it Hexproof or indestructibility or protection it dies
Yes, damage greater than or equal to the toughness of a creature kills it, even it is also a land, enchantment, artifact, or planeswalker.