Check in the Dashboard > Updates and click check again a couple of times so if that works.
Also on this site go to Accounts > Downloads –> go to Purchase History and click View Licenses and then click Manage Sites, check to see the your Site is included in the list. If not then add it there.
Odd – you can just download the latest plugin from your Account. Deactivate and Delete the current plugin, and install the new version. Don’t worry your settings will not be lost when you delete the old one.
No – it should automatically alert you for an update and allow this to happen. The only time it really becomes an issue is if the Site URL has been changed. This is not normal. Does this happen on your other sites?