I don't think the first two will be useful for this. Certainly you wouldn't want to be coding your own authentication systems in raw C, you want to depend on something known secure. Systems like the one I've been name-dropping already, LDAP, already exist to do things like this, though it's not a drop-in solution, there's a lot of fiddly bits.

Same goes for networking. ssh already exists and, as far as I can tell, is all you need for people to connect with ssh, so no need to play with networking in C. It's what scripts happen when they ssh into this system, and what login trickery is happening to let the accounts work everywhere, that's the question.

Of course, I don't know they actually use LDAP for what they're doing. I can't really tell.

Shell scripting will definitely be useful. Yes.. so if you want to find out how their system works, asking them would be a good first step.