When I close FAF client, I cannot start FAF client without restarting my computer

See subject. I don't know what causes it. It's very annoying.

Did you kill it via TaskManager already? Cuz smts it keeps running in the background -> Kill it, then it should open again as intented
(And make sure your TaskManager shows the 'hidden'/background programs as well)

Required rating for participation in balance talks when?

Just kill the task in the task manager. But yeah, this bug should get fixed. The FAF client is a mess, most of the time you close it, it stays open in the background and even increases cpu load.