That the new snapshot file becomes 00002, is expected. Because the 00001 already exists. So snapshot manager just takes the next available number.
Once you edit settings remove the disk from the VM (of course NOT delete, just removing), and you re-add the base disk, the VM runs from the base disk again.
Then it is save to delete the 0000x files from within Datastore Browser.
But the main problem here still is that your VM/ESX host does not like the snapshots.
Check the settings of your VM and mark the disk. Is the base disk maybe on "independent" mode?
I doubt, but just double-check.
Besides that, it is strange that your VM does not run on snapshots. It should be no problem to take a snapshot from the VM and powering off and on again.
As a test, create a new "dummy" VM (you don't have to install any Guest OS) on the same datastore. Play around with snapshots on this dummy VM and see if this works.
If yes, there is something in particular not ok with the other VMs. I cannot tell you what exactly. Maybe the logs have more details.