Get IP Address if Have Router Name & MAC Address?

Can I get IP address if I have router name & MAC Address?
If not with NMAP, then is there another tool to do this? Wireshark, maybe?

Are you talking about on a local ethernet network?

Yes. If router name and mac address acquired with Wigle wifi while on-site, can I now off-site/over internet, acquire external ip address to that router?

No you can not.