You may need to enable sylink logging on one of the affected clients to see what is going as opposed to one of the client machines that is working correctly.
1. Once the clients gets upgraded to the latest package, should we still keep that version under " INSTALL PACKAGES" for each client group?
If you plan to add new clients to this group then I'd leave the upgrade package
2.In the admin console, under Install Packages--> Client install packages, should we remove the older versions??
If the version you're upgrading from is not present here (to build a delta) then clients will receive a full package.
3. If the Super group ie Clients in the above senario has been assigned with 12.1.4013 and sub group : Desktops is assigned 12.1.6 MP5, which version will the endpoints take?
The auto-upgrade works independantly for each group regardless of inheritance. You can assign different versions to groups even though they may inherit from another. In your case, Clients will upgrade to 12.1.4013 and Desktops will go to 12.1.6 MP5.
Packages must reside in C:\Program Files (x86)\Symantec\Symantec Endpoint Protection Manager\Inetpub\ClientPackages