Re: Dumb question from a newbie
A VPN makes a connection appear to come from somewhere else. So let's say you start a VPN on your router and make it the default gateway, then all your connections to Google, Facebook and anywhere else would seem to come from the other end of the VPN. In this case it would be impossible to separate out which computer at your end made what connection unless you keep records.
Now, if one of the computers behind your router started a VPN, again all connections made through that VPN would appear to come from the VPN gateway. It is possible that the VPN gateway might keep a record of where that connection was started from but due the joy of NAT, and provided you don't keep records, it will be impossible to tell which system behind your router started the connection.
However, you should note that through things like browser fingerprinting etc it may be possible to tie a connection to a machine behind a VPN.
A proxy will also have a similar effect but with all of these things you have to hope that the provider either does not keep records or store traffic streams.
Also note that eg a US VPN will make you appear to come from the USofA and sites like Google and Amazon will give you the .com instead of your preferred country version with hilarious results if you buy stuff not noticing this.
That's a nasty cough you have. The air must be pretty dry down south ...