Your cluster will be down if your DC will be down as you are having 3 votes in the DC.
For Log shipping you need to manually bring the secondary db online to be accessed by the applications for read write connections.
You can use the AG for DR - that is what it is designed for...but to do that you need to be able to move the file share witness to the DR site to allow for a quorum.
You would normally setup the cluster with 3 votes for quorum - the primary and secondary nodes in the primary DC and the file share. The DR node will normally have a node weight of 0 so it doesn't participate in quorum to determine cluster health.
For a failover - you need to move the file share witness to the DR DC and change the node weight on the DR secondary and manually migrate the listener to the DR secondary.