At the height your jumping the dressage saddle isn't a problem, you don't need to rush out and buy a new saddle.
I jumped ponies back in the day when junior riders all rode in jodhpur boots. No such thing as half chaps either.
Children in pony showing classes in the UK and Australia still have to wear short boots, so your lack of tall boots or chaps doesn't scream out to me as being a problem
If your legs are getting rubbed then buy some thick socks - you can always cut the feet out of them and use them like leg warmers.
Your stirrups do need to go up a hole or two, you're constantly reaching down for them and that's destabilizing your lower leg.
If you're worried about the horse hesitating before the jump then ride in a light half seat and stay in that position up too and over the jump - at that height you don't need to be too far out of the saddle anyway and the light half seat will allow you to have more driving power than 2 point, without getting left behind.
You're sitting back too soon - that's probably related to the long stirrups, you getting left behind on take off and a general loss of balance and you needing to build up strength in your core and thighs. That will come.
One thing that really stands out on your horse is how overdeveloped the underside of his neck is. That's not going to help him have a nice, fluid, forward action. Your dressage schooling will help with that so well done you for making the effort