Here's my question, and I think the answer is yes, but I want to be sure, if I instal a mod will it effect my current game/saved games?
Skill mods (unless it's something like essence's rebalance) obviously won't affect a current game, but Items and room mods should become available as late as when the next level is generated.
Only if you turn them on. And all of them can affect the game, unless they add nothing more than skill trees; items, monsters, and rooms can generate if you add a mod to an already-running game.
Correct me if I'm wrong, but if you save a game with X mod activated, you must always reload that save game with X mod activated or you will crash. Not sure if this applies to Essence's rebalance or utilized skill only mods.
No, you aren't wrong. You have to load a mod you loaded before if you choose to continue from a save, because not loading mods which were used might result in item/monster/room/skill data missing, and that breaks the game.