Yes that’s called routing.
You don’t bind it to a NIC, you specify the destinations you want forwarded to each interface. Your VPN connection is just another interface.
If you’re looking for good docs, you may want to Google split tunnel vpn, and also bone up on your networking.
A few static routes should get you what you need
Raw disk access is a privilege in Linux, usually reserved for root.
You could have root change the permissions on the directory to allow another user or group write access.