Is it possible to change the location of the *.avhdx files in Hyper-V

When you create a VM that points to an AVHDX file and that file has no associated snapshot, Hyper-V will immediately merge-away that AVHDX. I suspect that you'll find that you already have only one AVHDX file, the one that the VM points to. You may already have no AVHDX files.

If you want to restore snapshots along with the VM, you have to do so by backing up the VM (and its snapshots) with software that will pay attention to those snapshots and recreate them on restore. This will be true of almost any backup application, like Windows Server Backup, or Data Protection Manager, or anything else, really.

You can even manually export a VM and then archive the exported VM, importing it later when you want to restore it. (A configuration-only export will avoid copying the VHDs, but if you can point the export operation directly at your backup media, you'll only be copying them once.)

What you can't successfully do is just save the VHDs and easily recreate a new VM later that is equivalent (even in snapshots) to the one you had before. A VM is more (though only a little more) than the sum of its VHDs.

Hyper-V Replica doesn't attempt to replicate checkpoints. It's a disaster recovery strategy for VMs, and it only replicates the currently running instance of the VM (and not the frozen moments in the past that those checkpoints represent.)

What Replica does do, however, is create checkpoints periodically while it does this replication. Each checkpoint that you see on the recovery server represents an application-consistent moment that you might recover if you do fail over. These don't exist on the primary server because you can't "recover" a lost VM on the machine that hasn't lost it yet.

You should be able to delete the checkpoint on the recovery server. I'm not sure why that's failing.