Okay... I'm not going to comment on the jumping bit since I don't jump
What I see is a lot of leaning.. your arms are kind of just.. flopping around or floating and not FOLLOWING his movement. I see him bracing all over and generally being very sour.
I think you need to work on your warm up. Do you have a trainer?
Warm up at the walk, getting him to loosen up. Gentle flexing, bending, circles, and figures (like serpentines, weaving, figure eights, spirals) when he's nice and loose, send him forward and do some leg yields on and off the track. Change direction often. Slowwwwwwwww downnnnnnnnnnn. You're kind of rushing through everything, when he's not really "with you" if you understand what I mean.
It's like you're chasing him when you trot, you were posting very sharply.
So relax.. soften your body, and don't trot until he's together and relaxed and loose at the walk.
As for contact, it's not consistent. It's loose-tight, loose-tight. Release.. JAB.. release.. JAB which isn't very nice on their mouths and also causes them to really dislike contact.
Change your arms. Your elbows can open and close. When you rise, they open up and your hands stay just where you left them.. when you sit, they close, leaving your hands just where you left them.
I can see a lot of things that, if they were smoother.. you'd be a very nice team.
If you don't have a trainer, I highly encourage you to find one. You'll improve in leaps and bounds once you target the things that need fixing.
But I really would work more on your walk before you trot.
And just so you know, I am not saying this is all you. Or your fault.. the horse needs a lot of work too but doing what I have advised would benefit you both as your riding directly affects him, and he directly affects your riding.