Have fun showing at that gong show, lol.
Jr/Am is referring to your age and status. Don't know why they aren't offering open but w/e. I'm assuming you're under 18? That means you're a junior.
Stable with, people usually just put their barns name, but if you're going with people from another barn then just list their names, or decide on a show group name and have everyone write that down to make sure you all end up together.
For stabling, it's just $45x2. Their day stall/night stall thing is tough to get used to, but basically if you're trailering back and forth it's $35x2 and if you're overnighting it's $45x2.
I would advise you to bring lights! Their show barn is really dark. Also bring lots of coolers/jackets and I hope for your horse's sake he is clipped. It's like -10C in the show barn and 20C in the ring.