1. Go to the Boulevard Scene, there's a Bank you can enter.
You can go to the Boulevard Scene by taking a walk to the streets, go to the street at your left, and walk against the invisible border. This will bring you to the Boulevard scene.
2. The number listed there is the amount of Prestige you need more than the amount you already have. Unfortunately, that number only counts the Prestige you get from Village Buildings. So, if you have 100 prestige from Village/Town Buildings, and 123 Prestige from setting free Prisoners, you need (200-123=)77 Prestige more than your current amount! (This was just an example.)
So the figure in the "what amount you need more" list only counts the Prestige from Village Buildings, but no worry! If you have enough Prestige (including Prestige from setting free Prisoners), you will advance in Class (that counter does count the total Prestige, not only the amount generated by Buildings).
Or at least in my experience.
3. I have that problem too. I think it's caused by the Native script for Siege Towers; Some trooeprs go forward to 'push' the tower forward, the rest stands back. The Siege Towers have been removed from the scenes, but I suspect the code for them is still there. I hope Quintillius takes a look at this and deals with it for the next patch (if he hasn't done already; He's good at killing those bugs apparently).
4. Weird, I never got that...