Sql-server – Need to configure Availability Groups between three different SQL failover instance

Prereqs, Restrictions, Recommendations - Always On Availability Groups states:

The actual number of databases and availability groups you can put on a computer (VM or physical) depends on the hardware and workload, but there is no enforced limit. Microsoft has extensively tested with 10 AGs and 100 DBs per physical machine.

An availability group is really just a container to group mirrored databases and associate a listener with them, and to provide the interface with Microsoft Cluster to determine what server should be primary. The only significant associated work is the replication of the databases.

So the short answer is "yes," you can use the same number of instances and databases, but you have to consider whether the additional load of replication will overload the system. So you'll want to pay close attention to the databases that have higher I/O and try to distribute them amongst the nodes so that one node isn't a primary and/or secondary for multiple heavy hitters. Or, if that's unavoidable, make sure you've got lots of bandwidth, CPU, memory, and disk space.

AlwaysOn Availability Groups, Listener, Named Instances, Port Numbers, etc. is also something that you'll want to peruse.

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.