So, one of my character just became a ruler (my first time ever), and I have a few questions. So I'll just jump right in:
1) Where can I change the government system of the realm? I am talking about the realm being a Tyranny, or Monarchy, or Republic, etc, and not the way council positions are elected. When I go to the government system tab under politics, I can only update the realm's full name, title system, and lord and council selection. When do I get to change the actual government system?
You don't.
This is only possible when the realm is in anarchy. There are two ways to get the realm into anarchy: either have it completely fail a ruler election, or lead a successful rebellion that takes the palace by force. (The ruler stepping down to let the rebellion succeed will
not result in anarchy.)
2) If I create a new duchy from a city that already has a Lord, will that Lord automatically be promoted to Duke?
Yes.
3) A ruler without an estate cannot found a new army, is that right?
I don't know offhand if this is true, but if it is, it's quite silly, and should not be the case. As far as I'm concerned, a ruler should always be able to found a new army. So if you find that you can't, please report it as a bug.