As far as I'm aware, the tax income and levy size you get from any vassal are based on their holdings, and modified by your realm's taxation/levy laws and the vassal's opinion of you (for taxes at least - I'm unsure whether opinion influences levy size). Catholic Bishops have the added complication of paying their tax to either you or the Pope, depending on who they have the higher opinion of. I don't think a vassal's statistics influence any of these things.
Pretty sure any male of your court can be appointed to the role of Court Chaplain - on appointment the character's portrait will change to show them wearing religious garb.
You're right that making unlanded son's Bishops counts as giving them land. Be careful with this though, as once made a Bishop your son is not eligible to inherit other titles from you in the usual way. If your main heir has an "unfortunate accident" you may find yourself suddenly lacking an eligible a successor!
For realms smaller than Kingdom, any lord can appoint a successor for any Bishop that is his direct vassal. If no appointment is made, the new Bishop is appointed internally by the Church (or Pope). Larger Catholic realms must opt for one of either Free or Papal Investiture - Free operates as before but angers the Pope, while Papal gives the Pope sole control of Bishop appointments in your Kingdom and grants you the Pope's favour (useful when seeking to excommunicate rivals, divorce wives and so on).
No. You can only vassalize nobles of lower rank. When you win the war, he will thank you and leave to rule Scotland, completely independent from your divine supervision. Drat!
The only way to vassalize a king, is to become an emperor. Emperors, being the highest possible rank, can thus never be vassalized.
As a sidenote, this also goes for titles that are achieved later. If your lower tier vassal gains a title that is equal or higher rank to yourself, he will leave your realm and take all his lands with him. For this reason, you must be veeery careful-like, when you give titles to people who are likely to inherit in other realms, or whose heir are ruling somewhere else.
Of course, this being Crusader Kings, you can do some scheming for a brighter future. When you invite him to your court, you can propose a matrilineal marriage to one of your dynasty. Since he is in your court, he will never object. That means, when he takes the throne later, his heir will be of your dynasty – this may require that any current wives and children experience unfortunate circumstances, resulting in their sudden departure from the mortal realm (deus vult!).
Now, if you're really cunning, you can arrange for him to marry your female heir, and thus two generations down the line, your grand heir will inherit the throne of Scotland. Of course, this won't work if you have any sons ... unless accidents happen or they are otherwise ruled out of contention.
Best Answer
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.