Photo 1) This horse is giving you a false headset and is very much on the forehand. Possibly because of the bit; is that a Kimberwick? Your reins are very uneven. Makes me wonder if you are doing the whole jerk with each rein individually to bring the nose in. I like your position here except I'd like to see you looking up and not down at the horse's neck as well as more heel depth.
Photo 2) Another pretty good position. Just nitpicking would be more heel and lowering your arm a bit. Bring your elbow back to your side and create a nice "L" shape with your arm.
Photo 3) Ahhh, showmanship! I was never very good at it. I had the horrible habit of always unknowingly pulling the horse's head in towards me. You look good though. I like that you are taking a big stride so you can show off your horse without holding him back.
Photo 4) Again, I'd lower you whole arm and bring it back.
Photo 5) Great position here. I like everything except for the arch in your back. Love the smile on your face. :)
Photo 6) No comment here as I do not do barrel racing and have some select things I'd like to say about it. ;)
Photo 7) This is how I'd rather see your arm! Now just pull your leg a bit more underneath you. Put your head up a little bit more as well; look around the arena.
Photo 8) Have fun!
Photo 9) Good job! The only thing I can say is when I was taught showmanship, we'd roll up the lead a bit more so there wasn't a big loop like that. Just tidies it up more I guess. lol