1. Don't the other warmongering counts/dukes belong to the De Jure HRE? Or, are they direct vassals of a certain kingdom or duchy? That could maybe explain why they can have internal wars.
2. Do you mean that the Pope hasn't called for any Crusade in many years yet? You were unlucky then
3. Never played as a vassal, but I guess you will only be able to set the leaders of your own troops, as usual, and in case your character is picked to be leader of your liege's troops, there should be a way for you to dismiss him, but don't know how though, sorry.
1: maybe they are party of a kingdom, but they are definitly part of the HRE
2: no, there are crusades, but I dont know how to join them. I cant declare war to the. I can look for the warscore in the upper left of the screen (how do I open the warscore in a normal war I'm involved or that I've started?).