How to configure multi-site SQL Server 2014 Always On Availability Group for DR
Yes the DR nodes need to be joined to the existing cluster. SQL Server 2016 has Distributed Availability Groups, which would a cluster at DR separate from the existing one, but you are on SQL Server 2014. The DR nodes should be able to see the fileshare witness. You can adjust quorum votes so that the DR nodes don't have a say  in if quorum is down. I do add a fileshare in DR for when we failover to it, but it's not part of the cluster until the failover occurs. 
The connection string would specify the AG listener and would not specify the two IPs. MultiSubnetFailover=True takes care of it by connecting to the IP that returned success first.
Yes it is very reasonable to swap roles. The last 3 companies I worked for had DR sites that we'd failover to 1-2 times per year, running production at DR for a few days and up to 3 weeks. Failovers are an offline event. They take about 15 seconds on AGs.