1) The only way to leave without dishonor is to wait for the time to reach zero, at which point you will automatically be taken to the next match (if you won) or back to the Random Arenas outpost (if you lost). Every other way of leaving (such as map traveling back to the outpost) invokes Dishonor points.
2) Alliance battles is probably the most similar to what you're talking about, but it does require a pre-made group of four, which will then join randomly with two other pre-made groups of four. Thus, Jade Quarry, and to an extent, Fort Aspenwood are control-point type matches with randomly formed teams. Jade Quarry I would consider more "control-point" like, as you capture shrines, guard posts, and quarries.