Which Italian provinces get ceded to the Pope on creation of HRE

The pope can let you:

1. Divorce your wife,
2. Get someone excommunicated, and
3. Grant "permission" to invade another Christian country (that's larger than yours) and take its top-level title.

The first boon is neat if you hate your wife (Didn't notice her inheritable hunchback, harelip, and stutter before you married her? She's trying to kill you?), but don't have sufficient intrigue, gold, and/or stomach for a risky venture.

Excommunicating your enemies is fun, because it allows you to do three things: kill them without repercussions if they're your prisoner, arrest them without being accused of tyranny, and it's an automatic Casus Belli - a legal excuse to start a war and take their stuff. Other Christians generally don't mind what happens to an excommunicated Christian.

Invading a (larger!) country lets you take its top-level title: Duke, King, Emperor, etc. So rather than nickel-and-dimeing a country, repeatedly forging claims and going to war to snip off a county here and a duchy there, you can simply invade that country and take the crown. The main trouble is that the country must be larger than yours; you may request an invasion of the Holy Roman Empire, but don't expect to win. Try to find someone that's just a little larger than your size. One of the game's traditional starts, taking on the persona of the Duke of Normandy, is exactly this: the Pope already gave you permission to invade England.

It sounds like the Kaiser has created an antipope. That means, that the bishops in the realm will pay taxes to the antipope instead of the old pope, and he will in turn give those taxes over to whoever appointed him. If the bishops don't like the new antipope, I assume they would continue paying taxes to their most direct liege (e.g. you).

There is a different question here on Arqade dealing with how to check the opinion between to NPCs. Perhaps that will help you figure out what's going on.