Hurdle is a bit high, and you turn slightly too early for my liking in the roundoff entry. You won't get deducted for either, but both are likely to contribute to subsequent deductions (fixing the hurdle/entry will give you straighter and more powerful tumbling in general).
First deduction that jumps out at me is the landing of the roundoff. Feet are apart (which is a deduction), and knees are also bending inward (which is not good for your knees long-term, as well as being inefficient); I would focus on seeing your feet together on the floor before initiating the backhandspring (literally, you should see them on the floor as you land the roundoff). This will help you get your feet together, as well as slightly delaying the backhandspring takeoff, which will give you a lower, more powerful trajectory on backhandspring takeoff. It will also make it easier to keep tight form in the backhandspring; your BHS has some leg separation and bend, but that's basically unavoidable because of how your roundoff is landing.
As for the back tuck, it looks reasonably decent for a new skill, but there is always cleanup to be done. Again, you want to land the BHS with the feet together and avoid any inward bending of the knees. Try to see the corner that you started in when you take off on the back tuck; you should continue seeing it until your knees block your view. Also make sure you are looking for the landing after you pass through vertical, and when you see it try to prepare for landing with the arms down by the sides; trying to land with the arms down by the sides will reinforce better landing-preparation technique, and give you a more vertical landing (right as your feet contact the floor, your arms should come up in front of you to hit a proper stick position).
My recommendations:
1) Passes of 3 backhandsprings from a stand. The first two backhandsprings should land with your eyes on your feet (which should be together), and scoop under as hard as possible; the third should land with your eyes on the wall, arms reaching towards the ceiling, and the feet behind you. Try to travel forward in the rebound at the end (if you do the BHS correctly you won't actually travel forward, but try to anyway).
This is to build cleaner and more mechanically efficient backhandsprings, as well as to improve the snapdown on your roundoff.
2) Cartwheel step-ins and roundoffs from knee lunge, trying to turn as late as you can in the roundoff entry, and finish with the feet together and in front of you, eyes on your feet.
This will help you develop a cleaner and more efficient roundoff.
3) Back tucks on trampoline. Arms up by the ears on takeoff (no arm swing), down by the sides on the landing. Your main focus should be on what you see. Watch the wall in front of you as you take off and keep watching it until your knees block your view; keep watching the knees until you pass through inversion; after passing inversion, look for the trampoline. There should be no forward or backward travel, and you should land in a straight vertical position with your arms by your sides.
This will help you build a cleaner and more controlled back tuck.
Congratulations on getting your back tuck and good luck at your first meet. I do not wish to in any way discourage your excitement about both of these things; however, the other users are correct in that there are some details in what you are saying that seem not to add up; USAG rules require you to compete at least one meet at levels 4-7 before you can compete level 8.