Greyed out menu options, broken activity monitor

The behavior you are seeing happens if you aren't recognized as having permissions to manage services on the remote server. This MSDN article describes some possible solutions on how to grant users rights to manage services.

Does the service account for the agent have local administrator permissions on the server? Have you stopped and started database services and the SQL Server agent service on the server since encountering this problem?

I had exactly this issue. everything was working fine until I noticed that the green indicator on the database cylinder logo (next to the instance name) became white instead of green (exactly as you have). Permissions were also fine. I restarted SSMS and connected again to the same instance and issue was solved.

This issue (remotely was white circle, locally was green) happened to me when I had multiple logins defined (windows integrated mode).

Some logins were through a windows security group that had the sysadmin privilege and another was through an individual account that did not have the sysadmin privilege.

The solution was to remove the individual account login that didn't have the sysadmin privilege. The green circle and menu options came back.