1. Getting reputation up as far as I can tell involves battling a bunch. I've found that when the odds are stacked against you the most, you get the most renown.
2. You can't capture towns, though you can capture castles--you can tell the difference because castles have those little towers on the world map. You can only loot towns, but if your army is too small the villagers will fight back.
3. You can't, and don't really need to capture nobles--sometimes they die, sometimes they escape to fight you another day. As far as I know, you can't really use any technique to always kill nobles as opposed to them being knocked unconscious and escaping.