1 - yes, but your approach is not practical. the snapshot functionality is meant to snapshot configurations, not a whole server. if you can model your application in a component template, you can use that to take a snapshot of your application and then deploy that. or you can use this to pickup differences in an update to your application.
2 - they take up alot of space on both.
3 - no.
Ok, That's what I tought.
I think I'll create an RFE for the local snapshotting since it's a nice feature. On the other hand I think it's quite hard to implement this. We'll see what support has to say