How can I test if an Internet connection is available via a certain interface? e.g. is my GSM(wwan0) modem connected to the Internet? If I attempt to run ping www.google.com - How do I know what interface is being used?
You could specify the interface.
ping -I $INTERFACE $DOMAIN_OR_IP_ADDRESS
ping -I wwan0 188.8.131.52
Using a known IP address will eliminate any potential DNS issues while troubleshooting.
How can I force connectivity via a certain interface if more than one exist?
You can set the default route. Static addressing with Debian, right?
/etc/network/interfaces with a text editor. Find the desired network interface and add the option
gateway x.x.x.x, where x.x.x.x is the gateway. Save and restart networking:
Otherwise, I believe one would need to use more advanced policy-based routing for this.