I taught myself some more about Knoppix and answered some of my own questions. I was able to view the IP address assigned to my network card (eth0), and I can see that it was assigned by the DHCP server. So all is well regarding my original question #2.

I assume that Knoppix is NOT handing out IP addresses, and that was just a little paranoia. So you can (probably) disregard question #3.

So all I really need to know how to do is access the internet from Knoppix via the network's Masqdialer server. I can browse the machines and their shared folders through Samba Network Neighborhood, so my machine is successfully talking to other computers on the network.