Well I'll try to answer some of your questions even though this is posted in the wrong forum. (I'm guessing a mod will move it eventually)
I've shown my horse in the Model/Halter for the last two years though I decided to stop though I am not opposed to showing a baby in the class.
Model Hunters is judging the horses conformation and suitability for Hunter classes. In most Over Fence USEF rated divisions you show your horse in a "Strip" class, no the horses don't dance for dollars lol, but you do take off your saddle and pad and jog them to show off the horses uninhibited movement.
You show in a bridle, typically a snaffle bit, though I haven't had a judge open my horses mouth to check the bit, you could essentially show them in anything that looks like a snaffle from the outside. Your horse needs to stand in an "open" position which is actually easier to set up then square which is what they do in AQHA and most breed show Halter classes. (Arabs and Gaited horses stand differently and are presented differently and you'd need to ask someone involved in In-Hand Breed Showing how that is like I said my experience is limited to Model Hunters.)
Gordon Wright once told a student to take up swimming because he would never be a good rider, that rider was George Morris.