1. My guess is just making short lightspeed jumps location to location. This is the first time it has every been introduced in Star Wars though. I read somewhere that Tie Fighters are equipped with the same hypersace tracking tech as the First Order capital ship in TLJ.
2. Definitely no direct answer. I think the fact that Emperor completely disintegrates from his own lightning might be part of it. He couldn't transfer his essence into her body because of that.