First off I'll say how lovely you ride your sitting trot, it is very soft and you look comfortable in the saddle. As you said your legs do need to come back under you a little bit, but that will come with time & more core control, lean back a little more to help reduce how forward you leg looks. If you focus on your abdominal area a little bit more (tensing ever so slightly through your stomach - but not so much you stop breathing!) it can help with your hands as you are a bit wobbily, a bit in both but a little more in your right hand. When posting use your belly button to pull you forward, your pelvis should be moving to your hands, not your hands to your pelvis. Act as if you are pushing a plate back on the table with just your pelvis, your hands are not allowed to move, and neither are your shoulders. This means instead of just going 'up' when rising you have a forward motion.
Not sure how you feel about his head carriage, but if you continue to push actively in trot and shorten your reins I don't see any reason for him not to come up into your hands (as in english they look for their poll to be the highest point).
Hope this helps and good luck!
It's nice to be important, but it's more important to be nice.