Are these socks washing machine and dryer safe?

Yes they are very safe! we haven't had a problem, no shrinking, no fuzz balls etc. etc. They A very good quality socks at that price, in fact I was just about to order another set. My husband loves them!! is very perfect.

is "8.5-13" referrring to sock size or shoe size? I wear a size 9 shoe.

That is just shoe size, it fits shoe size 8-13, is my understanding. My husband wears shoe size 8.5, and the 8.5-13 socks fit him fine.

are these socks thicker than normal socks? I have boots that are a little too big and require a thick sock.

they are dress socks so they are thinner.

Is the elastic band at the top stretchy enough?

I would say yes but it is not as stretchy as some socks. I found that they fit well, The fit is fine, material is good, The fabric is unique in that way. The top fits snuggly but the socks do not sag. Hope this helps.