I see both almsot every time I start the client.
If you can't join MM, can't see games or can't join them, look at your account name top right. If it's missing the country flag next to your rank, log off and log back in. That's usually enough to fix the session.
Sometimes one log off doesn't fix it, and in that case, no amount of logging off and back in fixes it. Close and reopen the client. For me one restart usually clears that issue.
For the client not closing properly, for me it happens every time I watch a replay. If you open the client, play a single game and close the client, does it close properly? If you open the client, view a replay and try to close, does it hang every time?