1. I think Nausea is counting as disease and can be removed with a Level 24 Cleric Spell.
The Curse can be removed with a level 36 Cleric spell.
It's probably a good idea to…just live with the curse until the cursed dogs are gone and then let the priestess do her work.
2. There is a specific item for each god. It's not random stuff.
But if you want to know the exact items, you can check the steam forums, there are people figuring out what use the special items have:
http://steamcommunity.com/app/296570/discussions/0/35221031514450025/#p1