It's random, but the monsters are on the third level (the small one), along with quest items if applicable. In my game, the first dungeon had 3(!) in a very small area, the second had 2, and the third had none.
No, monsters do not respawn in the battlefields, altho there are separate battlefields for each act with new quests, monsters, and treasures in each one. A good tip, if you leave your items in the bf like I did, make sure to retrieve them before the next act. You can trade for arrows or charms, jewelry, etc. to reduce encumberance and retain most of their value into the next act.