1. You can take Rome, but as long as there are living cardinals, the pope will respawn. I havent tried / read about the extinction of all the cardinals and thus the pope.
2. You can convert the populace of any region to your own faith, but your faith cannot be changed.
3. Depends on difficulty and your very personal experience. On VH I am in war with everyone but the pope and the feeble HRE as soon as we share borders. Stable alliances have been reported by various people on various difficulty levels. The easier the game the more stable should be your diplomacy. On VH its hard to maintain good relations and thus you will get stabbed in the back, by neutrals and allies alike - as soon as they see a chance ( and the AI is not very demanding on those chances hehe ).
4. No outrageous results for me so far on VH. Only saw a small number of battles where the underdog won, has a rather good feel about it. Not that random to me.
5. At the beginning its quite hard, especially for factions like the HRE. But later as you gain more cities your surplus can easily get into the tens of thousands. Right now I have about 40 regions and have more money than I need to keep all my settlements constructing needed buildings continously.
Overall it is easier to keep huge cities under control so they make good money. As the English I run a 40k population Jerusalem with 4 garrisoned units, no general - on low taxes and 96% christian faith. Capital is Dijon in easter France.
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