Several places to look for:
1 At the Pi, look at syslog: sudo tail /var/log/syslog -- when it is online, you will see messages from the TTN-Gateway (might need to look beyond the last few lines).
2 Go to http://thethingsnetwork.org/api/v0/gateways/ and use the browser to search for your gateway UI.
Re Wifi: This is the one I use: http://thepihut.com/collections/raspberry-pi-wifi/products/usb-wifi-adapter-for-the-raspberry-pi
So far, it does what it should, but I have no experience with long-term stability.