Is it supported to run 2-3 app volumes managers all pointing towards the same Microsoft SQL database? The SQL instance would not be using AlwaysOn.
Yes it's supported and I belive it's the only way to get High availability on the app volume manager.
Here is a link descibing how to set up and scale the App volumes manager.
Depends on what you mean with multiple Appvolumes managers.
Do you mean to have a loadbalancing cluster and HA abilities so one of the Appvolumes manager can crash? Then yes not only is this supported but also best practice to build it like thta.
If you mean multiple instances of Appvolumes, that would also be supported but make sure to create different databases for each and every instance of Appvolumes. Otherwise you might end up with strange behaviour.