Don't use the same private key in two places at the same time. This means it's not a good idea to copy private keys between computers and use it in two places, and probably also means you shouldn't assign the private key to two interfaces on the same computer at the same time, unless you have a really particular and weird setup and know precisely the implications of it. Doesn't sound like that's the case here. So you're probably best doing a private key per interface.

Yes. It explicitly doesn't do it.

Please let me know what I need to add to wireguard.com/install/ in relation to VyOS's support.