Wait, so if I use qcow2, then I could rsync those files somewhere else?
yes, you can simply rsync qcow2 files since they are normal files (note that you must not do that while the vms are running, or you'll get data corruption)
Would I still be able to use LVM, or would I need to use something else, to rsync the individual qcow2 files instead the whole lvm volume ?
i don't get the question, lvm and qcow2 has nothing to do with each other. qcow2 files are files, lvm is a block level storage (no files)
Lets say I have a backed up qcow2 on external nfs storage, then I create a new proxmox server, would I be able to connect that nfs storage to the new proxmox server, somehow regsiter my vm, and see the snapshots ?
not completetly, in addition to the storage level snapshots, we save the snapshots in the config file too ( e.g. /etc/pve/nodes/NODENAME/qemu-server/ID.conf) these
config snapshots are the authority for showing snapshots in pve (and the names correspond with the snapshots on the storage layer)
this is done since the hardware config of the vm can change between snapshots and to correctly rollback the snapshot it must be the same as when taking the snapshot (when ram is included)
that's another thing, if you take snapshots with ram, for each snapshot there is a volume on the storage for that (which you must also copy)
How does clustering effect this ?
Like if I have a regular cluster, and I migrate a VM from one node to the other, do the snapshots go with it ?
If I have a High availaibilty cluster, do snapshots created on one host, automatically appear on the other host ?
this depends:
if the vm disks are on shared storage, there is nothing to migrate so it works.
if the disks are on local storage, we should always be able to do that for offline migration, but for live migration it depends on the storage (won't work for qcow2, but for zfs AFAIR)
EDIT: to clarify, HA will only work for shared storage (or for zfs replicated vms) HA with local storage cannot work, since if the node is down, you cannot recover it from the other ones