Keep your upper body still, mainly follow with your arms/hands. Although you want your whole body moving with your horse, don't bob forward with your whole upper body, just let your hands go with his mouth. Also, keep your heels down and hands together.
At the trot, you were constantly bumping him with your heels. Try to keep your leg still and then when you start to feel him slowing down urge him forward with being a little more forceful with your posting and squeezing with your lower leg. If he doesn't respond, kick, then give him a smack with a whip behind your leg! Constantly bumping him with your legs dulls out the horses response to your cues. Your goal with riding should be to ride with the least cues possible, and make it hard for people to see you cueing your horse forward.
With collecting, rather than just using your rein, move him forward, INTO the bridle. You may be trying to do this with you bumping him forward, however, in order to get them moving into the bridle using their hind end you need more of a squeezing effect. Like, squeeze for one thousand, two thousand and release, until you feel his hind legs engaging under himself. He does seem heavy on the forehand, which can be helped with lots of transitions and leg yields.
Sit up straight, keep your elbows bent, and don't lean back! Does seem like your stirrups are a little short, could you let them down a hole or two? Good luck!! You guys seem like a great match, and I love how you look up :)
“Good things come to those who wait… greater things come to those who get off their ass and do anything to make it happen.” - Unknown