I thought that it was the drivers, so I updated them through Nvidia Experience, it didn't helped. I tried to verify the files of the game through steam didn't help either...
Looks like a connection issue (routing issue). Sometimes problems like that solve themselves in a couple of days. You can try using a VPN and see if connecting through a different country works.
Same problem here since 4th Februarym wheb it starts (if it starts at all) then I get an error 13 trying to refresh server list, abd sometimes an error 503 when starting the game tryed changing DNS on windows, reseting router, reinstall... hope it get fixed soon ;(
If it didn't fix itself in more than a week, I think chances of it happening are getting lower and you should try a VPN to see if it helps.
No. They'll ban you only if you use it to exploit their regional pricing feature or circumvent region-locking. Simply playing games won't do anything. Someone even got a reply from Steam support that confirms you're fine: https://www.reddit.com/r/Steam/comments/73iop4/usage_of_vpn_is_not_strictly_prohibited/ * - That exploit doesn't work anymore anyway.