Eldritch battery/CI

when you get it does it apply the ES recovery to your mana regain or no.. and on CI does mana get converted to ES or just removed?

I'd appriciate any information still kinda new and trying to get a decent build

Eldritch battery will drastically increase your mana regen if you have a large energy shield. I do not believe this is due to ES regen carrying over, but simply by the fact that more mana = more mana regen. You can achieve ridiculous mana regen with it.

With chaos inoculation your life drops to 1 but you become immune to chaos damage, which is a type of damage that normally pierces energy shield and directly damages life. You keep the same mana / ES.

I don't really advise you to get either of these two keystones until you are high level.