If I'm connected to a wireless network and then additionally connect to a private VPN, can all my web browsing activity be logged through the VPN? if I use Safari in "Private Browsing" mode, will each website I visit be retrievable by the network that's running the VPN (which is distinct from the network providing me the webaccess)? thanks
A VPN only creates a tunnel between your computer and the end point of the VPN. No one along that path - like your ISP - can see what you are browsing. However, that encryption ends once you enter the new network. The endpoint network has become your gateway and is providing the DNS resolution, so therefore they can see what you are browsing and all the (unencrypted) traffic your sending and receiving.. "Private Browsing" and its equivalents in other browsers will not hide your anonymity from the network you are on.