AlwaysOn AG: Current Host Server - Owner Node - Primary Instance
Should the "Current Host Server" the same as the Owner Node of the AlwaysOn AG?


That's the node that is currently hosting the  core cluster resources, it isn't the same and is just another role. Different roles can be owned by different nodes. In this case, they do not need to be the same - and generally most people don't care who owns the core cluster resources in a WSFC that only has SQL Server. It does make a difference in certain situations but for the vast majority, it makes no real difference.


  Imagine if I want to maintain a host. Shall I first failover the AG (via SSMS or with ALTER AVAILABILITY GROUP...) to the second node/another node and at second a failover of the WSFC-Current Host?


If you're going to be maintenance to a host, I'd move all roles (drain) off of that node. So, yes, everything should be moved from it.