IF you use a Bridge connection between the guest OS VM and the Host OS as I described above, the DHCP server on your router will assign it an IP address within the dhcp pool range that your Host OS is on......Bridging basically takes the guest vm private network and joins it to the host os private network, making it one big internal lan private network. The Nordvpn resides on the public network facing the Internet side on the host os.
Since you are on the same ip subnet after the two private networks are joined, you can ping back and forth between the vm guest os and the host os. I enable ip routing on my vm guest Oses and the host OS, but it's not really necessary but it doesn't hurt anything to do that.
so this answers your 2 questions.1. IP traffic will be routed from the guest os to the host os to the internet over the vpn connection to the internet and 2, NO you don't need to install the vpn on the guest VM OS.