Is Cat o' the Cannals immune to every opponent effect? Does that include plot cards? Does it also mean immunity to Stealth? Sorry for this newbie questions, but I don't fully understand the meaning of "effect".

Yes, keywords count as card effects. The only way for an opponent to really get Cat is through claim (or possibly manipulating someone into killing her with their own card e.g. flipping Valar at some point). For more discussion see here. Also, Pyat Pree's effect still counts as claim and can be used to kill Cat (see here for more about that)

Thanks a lot!