Just a comment on the "right vs. wrong side" subject. I was always taught the left side was the correct side to mount/lead when I started riding. But now that many years have gone by and I am training my first horse (well, with the help of a friend and her trainer) I've learned that horses should learn everything from BOTH sides.
Why have a one sided horse when your horse should lead equally well from both sides, mount from either side, etc.? When I do groundwork with my yearling, I try to work both sides equally. So even though left is the "correct" side, I think most trainers will agree it is important to work a horse equally from both sides. At least that is what mine has taught me.
So I would keep doing everything from both sides, and if someone questions it, tell them why.
Beautiful Appaloosa by the way. I love colorful horses.
Just have fun and enjoy your horse (as it looks like you are). I will agree the breastcollar doesn't fit well at all if it keeps sliding down like that. Something with a neck strap (like an endurance or english breast collar) might work better. I do think a breast collar is a good idea as it can help keep the bareback pad from rolling under the horse in an emergency situation. I have had breast collars save me from rolling under the horse (in a saddle) twice now. I am a big fan of breast collars because they can keep you from rolling and sliding into places you shouldn't.
PS. Looking at your breast collar again, you might be able to add a strap to the rings that are on it, to go over the neck and keep it up on the horse's chest where it belongs so you don't have to get a new one.