When I open my OSX System Preferences and look in networks, I have open connections in both places: Host-Guest, and NAT. Is this normal?
Yes
Also, when I installed Vista in Boot Camp, it needed my wireless router code before connecting online. When I installed Vista in the image file, it never asked and connected online without needing to enter any code. Is this normal for the image file installation?
This is direct connection in case of Boot Camp
Incase of Parallels Desktop you are using NAT on Mac side, and Mac is NAT for your VM
