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 !