Failover Cluster, Availability Group, and Disaster Recovery
Is our understanding that all nodes need to be on the same Windows Failover Cluster for Availability Groups to work correct? We read it here but aren't fully sure of what's being said.


Yes this is correct. Although starting from SQL Server 2016 you have Distributed Availability Groups in which replicas can reside in different WSFC


  Is it possible to set up HA in this manner? Where Node1/Node2 share resources but Node3 has a separate instance which cannot ever be a part of Node1/Node2.


Yes this is very much possible and I have this in my environment. Please note that in this case you would not be able to leverage automatic failover of replicas from SQL Server FCI to standalone node 3. You would have to reply on manual failover. This is because the AG replica resides on FCI which has its own failover.