Swimming technique baseline

This week was a bit hectic and I didn't get a chance to go swimming until today. The only place with a pool that I could use early in the day was one of the Goodlife gyms where I have a corporate membership, but unfortunately it has a tiny 10m pool where you get to do a hundred of laps to bank in a 1km workout. Better than nothing, especially since it was empty, all for ME, ME, ME! I could go in zig zags and circles if I wanted to, so that was on the upside. My coach gave me a few drills to work the Total Immersion technique, all with funky names like skate, under-skate, zipper-skate - well, I did a few hundreds of those, then 500m freestyle and at the end I asked my hubbs to take a video of me so that my coach can critique me. Feel free to let me know what I do wrong as well, I am here to learn. This was only the third time that I was trying this technique, so I know I need much improvement.

What I think I need to improve is the following:
-more relaxed and smaller arm movements. This is hard because I was taught to use my hands vigorously while swimming before and this is counter intuitive for my brain
-flipping my body on the side when I breathe. I think I rotate my body too much, but because of all the skating drills where you get to breathe pretty much on your back, it's not easy to find the sweet spot.
-continue working on the bilateral breathing
-more relaxed head position in the water. I know that I still lift my head up to breathe sometimes, so I need to become less stressed about not breathing long enough, efficient enough or swallowing water.

That's about it for today. I hope to be able to go and work all this in a "real" pool next time. At least 25m wouldn't be too much to ask, right? If only time permits, because the 25m pool only has the 9-10pm window open for adult swim. Quite a shame, we need more pools!