Do ALOT of squats.
Also start with 5 minutes of a posting no stirrup trot like every ride for 2 weeks and then after those 2 weeks progressively build up how long you can post your trot with no stirrups, it's strengthens your legs ALOT and I have done this and I can now go 25 minutes with out stopping doing a posting stirrupless trot, it takes a while but it helps SO much plus a lot of people will be amazed and compliment you!
I would practice sitting trot without stirrups or better yet bareback. This would encourage heels down and calves molding to your horse properly,and the toes in encourage balance. Imagine your legs are fluid, which would gather in your heals.
Hey so with the kicking, try to see if you can give him one big kick and if he moves from your leg, reward him. If not carry a crop and one big kick, if no response then kick and crop, even if he takes 1/2 a step forward reward him. You shouldn't be needing to kick all the time, this will make him dull to your leg and when you really need it he will just ignore it. Maybe try walk to trot and back to walk transitions as this will make him listen to you leg signals. Also with the toes pointing out, its not a crime! Don't worry, try getting your heels down and putting your lower leg (calf down) on the horse without squeezing, this should help. Maybe with the swinging try shortening you stirrups up a hole, this may help. Hope this helps!
When you rise and trot keep your heels down and use your knees to hold on and make you more secure if you know what I mean? Also when you are rising make it soft and in time with the trot don't bang down really hard and go at all different paces.