Search “what is my ip” on your web search engine to see without and with a VPN connection, to see if you’re really going through the VPN tunnel. Seems like you aren’t.

Video games, because it’s easier to do it legally. If it was as easy for other media, I would do it that way.

Well, your Guest Wi-Fi can either have access to the pihole server and have its benefits, or point them to a public DNS. You can’t block access to the dns server for your guest network and hope it works - because it’s blocked. Personally I’d give Guest Wi-Fi a public DNS, as you won’t have much fun when an app of your friend’s stop working and you have to fiddle and work it out.

If you point the guest network’s dns to the gateway, that gateway needs to know what to do with those requests. Either it has a resolver locally or it mist forward it elsewhere.