Yes, you would upgrade the SEPM, then the client.
Yes, the 12.1 SEPM can manage 11.x clients.
If you're going from 11.x (which is Enterprise only) to 12.1 Enterprise, your clients won't update automatically. If you have 12.1 Small Business edition, I don't believe you can it migrate the SEPM from an Enterprise Edition to a Small Business Edition. SEPM 12.1 Small business will (as I understand it) auto-update the client software the first time it checks in to the new SEPM.
Installation and Migration Documents for Symantec Endpoint Protection 12.1
http://www.symantec.com/docs/TECH163707
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