upgrade the mirror server (i think it means the server that runs the database with mirror/synchronise and restoring) right?
Yes correct. This means the server which holds the mirror database which is in recovery.
manually fail over to upgraded mirror server (does this mean failover the principal to this mirroring server after the updates?)
Yes correct, post upgrade of mirror server, you would also have to update principal but to do that you have to make it mirror. Hence you need to failover to mirror also this is part of upgrade.
Resume miroring (Does this mean it miss the steps to pause the miror before steps 1?)
Yes, as a best practice, pausing the mirroring is advisable.