I've never knit cotton socks. I think elasticity is a bit of a problem with them.
Seems like you could knit an elastic thread in with the yarn, though, wherever you wanted extra elasticity, like in the cuff.
Yes, you can reinforce it with sock nylon.
The socks I'm making right now are my experimental-yarns socks. I've got 9 different kinds of yarn in the sole, to see which will wear the best!