Okay.... I did not think you set your horse up for that trot at the beginning at all.
English riding (I am not experienced with Western) is about preparing your horse before and THROUGH transitions.
Her walk wasn't that great, and you had no true forward direction.
Her trot is lovely but that two point is scary...... because your legs aren't underneath you so would likely tip over and smash your nose if she were to stop suddenly.
2 point isn't about the angle but being balanced over your legs. In order to be balanced you have to find your sweet spot which means legs underneath you and to compensate you may have to fold your upper body a bit to keep with the horse's motion. Does that make sense?
Your posting isn't that bad for first go at English. But like others have said you need to post towards your hands and AS you rise (which should 98% rely on the horse's momentum pushing you up) you open your elbows so your hands don't move. When gravity brings you down (again...98% is gravity) you close your elbows so they stay in the same place. Do not bring your hands up with you.. they stay down. An exercise you can do is extending your pinkies down till they touch your saddle pad and keeping them there as you post. You will feel yourself trying to balance on your hands via your pinkies being squished.. work on feeling no change.
You are tense probably because an English saddle feels like your horse is naked in comparison to a western saddle. It shows mainly in your sitting trot and how you feel grabbing for the reins. Only do as much as you are comfortable with. Grab mane as you transition to help you not catch your horse in the face (which is still AS annoying to them as catching them in the mouth)
Please do not cross the reins over her neck. Each rein stays on its side.
:) Not bad for your first time, and you two look cute! But I guarantee if you work on those few things I mentioned that you'll feel much more confident in such a different style of riding.