First time going to the track. Any advice?

Nothing wrong with that all for a first passes down the track.
What rear end ratio? What launch rpm and technique? Kind of sounds like a small highway gear and did not see much wheel spin, although it’s hard to tell. Nothing wrong with highway gears, just wondering.
In the video driving to work, it kind of looks like the steering wheel is almost 90 degrees turned to the right while you were driving straight. If so, get the front suspension and steering linkage looked at really well and get a front end alignment. Get a print out with readings before and after. May be possible everything is fine and something was installed crooked.