What is the overhead performance penalty for running Session State Server instead of InProc? Is it significant? I understand that you can restart w3wp with the state server and retain all session state - is that the only advantage over InProc?
It depends on your deployment plans: on a single server, the penalty is small, but the benefit is equally limited: your session state survives process recycles (as mentioned) but that's about it. You'll have some cross process marshalling with StateServer mode, so expect some additional cpu load, nothing too impressive.
In a web farm/load balanced setup InProc won't work, unless you can configure sticky sessions/server affinity. Be mindful of the fact that the StateServer node itself can become a single point of failure, so be sure to compensate for that. Having said that, the latency of a StateServer is in general much less (= better) than when you use SQLServer mode.
Make sure that your code/site gracefully handles lost state, regardless of where you store the data.