Why are you so sure there is a Mission 10?
Near as I can tell, all 3 of the factions have a 9 mission campaign. There's nothing wrong -- just bad UX that makes it non-obvious that the campaign is over.
The full campaign mission list is as follows:
Von Esling Airbase
Checking online, it appears that the Leningrad mission is the last mission of the Allied campaign. There is no mission 10. So there might be a bug in that it doesn't return you to the campaign selection screen, but it's not a bug in that it doesn't start mission 10, because that mission does not exist.
If the game is crashing the network, it is possible that the drivers are out of date OR the software used in the game is conflicting with his native drivers and causing a crash. My PC crashes a certain program whenever I plug my headphones in, as an example.
Things to try would include:
Updating drivers for the networking device = check the manufacturers ...