I understand what a VPN does, and I understand the concept of tunneling between the end user and the VPN server to allow this secure connection to happen, but what happens after that is somewhat vague to me.
Can any node on a network (i.e. network host) run a VPN server? I.e. it makes no difference if it's a router or a simple device connected to the router (that is accessible from outside)? And is it after the tunneling step just like a proxy, in that the VPN server captures the packets, and then resends them itself and returns the response to the origin?
Another question: Do packets forwarded by the VPN server contain the VPN server host private IP, or does the VPN server software act as a new node on the network and receives its own private IP from the router?