For the downward dog slip - I lay a towel flat out over my mat for my hands. Sounds simple, but makes a world of difference. My last mat was slippery as heck; combined with my sweaty hands, that was a recipe for disaster!
I also have barre socks with grip which also prevent sliding. Fair warning though, they can tug at soft delicate yoga mats but if you have a hardy mat, or no mat at all, they're great!
I looked and couldn’t find them either. These look like a close dupe from lululemon.
https://shop.lululemon.com/p/womens-leggings/Nulu-Colour-Block-High-Rise-Tight-25-MD/_/prod10643238
I also found these amazon leggings (i have other leggings by this brand and they are great!) that are similar-
QUEENIEKE Women Yoga Pants Blocking Mesh Workout Color Running Leggings Tights 8030 https://www.amazon.ca/dp/B0948G1LX9/ref=cm_sw_r_cp_api_glt_i_0EYK0HHBZBCWYK6WG9RW?psc=1
Here's what I bought:
https://www.amazon.com/gp/product/B07NQ5MWF2/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1
You probably know this since you bought the similar ones. They look more substantial in the photo than they are. They look in the photo like they might hold their shape without a foot in them, but really they are a sock but with the grippy bottom cut out heel. The ones you mentioned are sold out everywhere, but I think these are better for me.
I couldn't even sit on chair for more than 10 minutes due to backache three month ago. Then I started doing stretching exercises and push-ups for 15 minutes a day. After a month I was able to do about 3 push-ups. It was of course hard at first but using some mobile apps(a lot of great stretching apps and habit making apps can be found in app stores) really helped me to have more discipline. Today when I was doing my daily exercises, I was able to do 12 push-ups and also did the headstand. So I suggest doing daily stretching exercises with a mobile app, alongside yoga.
This is the one I used: https://play.google.com/store/apps/details?id=stretching.stretch.exercises.back
I really recommend The Yoga Sutras of Patanjali
The wife and i have been doing yoga with adriene and love her so much!