Updating mongo sharded cluster without down time for mongod
All details are here: http://docs.mongodb.org/manual/release-notes/2.6-upgrade/

Answer 1: All metadata will get updated. I suggest to execute the mongos --upgrade using an extra mongos

Answer 2: You don't have any downtime from the config servers since mongos have the require cached information and balancer is disable

Answer 3: There is no other way. You upgrade the secondaries and then promote one of them to PRIMARY and upgrade the old-PRIMARY. Downtime is minimal (1-2 second my case) if replica set are well-sync