Heh, I think you guys are giving my opinion too much weight, I'm just a guy who's been to LS too many times and doesn't mind helping first timers
I checked out some of your videos, you're doing pretty darn good for your first track day. I don't think I got 2:03 my first time at LS. Anyhow, some notes on your TT lap:
Turn 1: Looks good, I shoot to buzz the checker flag station right by the wall
Turn 2: I found the double apex line to be the one that doesn't upset the car, plus it gives you an extra carlength or two for braking. On your time trial lap, looks like you had a bit of braking before you tracked out to the braking markers. I don't brake there because it seems to make the car angry and screws up my braking zone later because of weight transfer. I track out to the brake markers, get the car in a straight line parallel with the 1st apex, and then brake, brake past the apex, and then turn in for the 2nd one. The single apex is much easier to teach
Turn 3: Looks good, just don't early apex it
Turn 4: Can't really tell since it's washed out, but looks like you're using all the track out which is good.
Turn 5: Your apex could be a little sooner, which makes you not track out soon enough. Don't have to worry about the sound booth in the Tesla, lol.
Turn 6: A little trailbraking here looks like it upset the car coming into turn 6, but not too bad. Line looks good, you can carry more speed through here than you think. Mind the bump at the apex!
Turn 7/8: Looking good through here.
Turn 8a: Keep the wheel straighter for just a bit longer, it allows you to put down more power and track out more to the left.
Turn 9: The most difficult, I'd keep the car pointed at the flag station just a tad longer and then turn in. You know you're doing this turn right when you can set the steering wheel lock on turn in, hit the apex, and track all the way out without adjusting the wheel much at all. This will point you right at teh #1 brake marker for turn 10.
Turn 10: I like to get on the rumbles for the apex, and then track all the way out. Try getting closer to the apex, plenty of grip down there.
Turn 11: Keep the tires off the paint under braking, and get it all done in a straight line, no time to be made up trailbraking here
This also pisses the car off less past the apex, letting you put power down sooner. Since you're not in a miata, you don't have to get your picnic basket out for the front straight.
Obviously the smoother the better, but looks very good for your first event.