The GS105 should be fine and the problem is more related to the software side in my opinion. I have never tried to connect a mac running 7.1 but it should work. All the protocols exited at the time of 7.1.
You should make sure that you have installed all the network packages of system 7. What you will need here is the TCP/IP control panel and make sure that the right ethernet card is selected (it should say "connect via") and that "Using DHCP server" is selected. When you are using a DHCP server, you don't need to specify any IP address, mask etc., the switch and the OS are doing that for you!
As for the linux system, it is installed on the mac pro. The LC III is directly connected to the mac pro. An intel mac is much better to run this kind of virtual machine. It will be much faster. Anyway, you don't need a virtual machine to connect a powerpc OS X mac to a classic mac. It works straight away because appletalk still exists on the old versions of OS X.