I used to manage a ranch in Utah and we had 150 horses! The reason I tell you this, is so you know that I have experience in this field. The problem with dirt in a stable, is that when hoses eat, they spill feed on the ground and then eat what has fallen on the ground. When they eat of the dirt, they inadvertently eat dirt with their feed. This will cause sand colic and can kill your horse! So, no, never use dirt in your stables!!!
I suppose you could, although obviously it wouldn't be the first choice, the reason being that when stomped, it can harden and no longer be lovely soft bedding, and the many forms of bacteria that can easily make their home there. I'm almost completely certain that hay or straw is more preferred.
Definitely not. In addition to what has already been said, after a few months if urine soaking into your dirt floors, your barn would stink and be hard on the lungs of everybody. I've used everything, straw, shredded paper, shavings and sawdust. My personal favorite is pine pellets. If handled correctly it works best for odor and ammonia control and it has less waste when cleaning.