why do mateial--are these cotton

These socks are 91% cotton, 7% nylon, 2% spandex.

This is what I'm looking for, but I need them to have non slip soles. Does this company have that?

Not sure if you found an answer to whether this company sells non slip soles, but I needed them too and found this youtube video that showed me how to do it myself! Hope it helps you out as well! :) https://www.youtube.com/watch?v=KFUM9ceoKS0 If you're not comfortable following this link, here's what she did - she painted with fabric puffy paint on the soles! I tried it and it worked great, but I also painted on the top and sides of the sock, as they tend to rotate around my feet as I wear them throughout the day. I also didn't put as big of dots as she did, as I didn't think they would be comfortable to walk on. Anywho, hope that helps! :)

Are these socks safe to sleep in?

I believe they are safe. I sleep in my socks and I've had no problems.

Will these fit over a surgical cast?

Be sure to measure, but this sock is the perfect covering for my below-the-knee-to-toe cast! The sock material is stretchy and comfortable and completely covers all areas of the cast. The sock prevents sharp areas of the cast from directly scratching/cutting skin (which is quite painful), and it also prevents damage to bedding and clothing. I highly recommend this item to anyone who needs a cast cover, and since two socks are provided, there is even a spare!