Hi, just a quick question.

When an investigator cannot be cursed (for example, when they have Father Iwanicki as an ally), does it also protect them from losing their blessing from a cursing (Like Yig's start of battle ability)?

Yes. "You cannot be Cursed" means you are immune to all effects that read "You are Cursed", and so you would keep your Blessing as long as you don't roll a 1 on your upkeep !