‘…has performed an illegal operation & will be shut down immediately’ may not have anything to do with the network. Please provide the detailed error info the next time it happens.
See MS KB Article Q216171, Server Performance Degrades During Work Item Allocation, at http://support.microsoft.com/support/kb/articles/Q216/1/71.ASP? for the solution to the second problem. I think I would fix the second problem first just in case it was related to the first problem. Larry