As the title suggests.

What abilities/features/enemies in this game will pass on to the next?

Full Thrust is already in the FFXV demo when you equip one of the spears.

Hallowed Ground is kinda new but in past FF games you get a similar effect when you use a Hero, so I'm not sure if it's original enough to see it in the future, who knows.

Maybe we'll see Holmgang and Dragon Kick in the future.

Also is the Avatar an XIV original? If it is that's definitely something we'll see in another game.