2) How exactly does adding provinces and countries to the HRE work? I'm having trouble figuring out the criteria.
In general the province has to be
- In Europe
- Christian
- A core of the country doing the adding
- Adjacent to (or in the same sea tile as) a province already in the HRE
To join the HRE, you have to add your capital, which can only be done if you have high relations with the emperor (or you're the emperor).
If a country has a HRE province but their capital is not in the HRE, they're not in the HRE. If their capital moves into the HRE they get forced into the HRE, so there's a strategy to force larger nations into the HRE through abusing the capital mechanic.
If a HRE country has non-HRE provinces, they will only add those into the empire if they have high relations with the emperor, at least +100.