1. Do the NetApp backup offerings communicate with vCenter and is it vcenter that produces a VM snapshot which the array then copies? How exactly does the mechanisim work?
Yes, if you use Virtual Storage Console (VSC) this is a plugin to vCenter and is fully integrated into it. VSC/SMVI will take a NetApp snapshot of the NetApp volume containing the datastore(s) in which the VM lives. It is optional when configuring the backup in VSC whether you also create a Vmware Snapshot to quiesce the VM before taking the NetApp snapshot. VSC will do this for you should you wish to. The Vmware snapshot will be merged back once the backup is complete leaving you with just the NetApp snapshot.
2. If SMVI can produce an application-consistent snapshot of a VM, do I still need to use SMSQL to backup my DB's? What are the benefits (if any?)
You should still use SMSQL. SMVI/VSC creates a snapshot of the VM, but it doesn't do anything to quiesce SQL. The data may be backed up, but it is a crash consistent backup of the database(s). I tend to think of VSC backups as backups of the OS itself, while SnapManager backs up the application data.
3. If I take a backup of a VM in my one data centre, which I then retain for quick recovery, can I also replicate that backup to my other data centre using SnapMirror? (Thus taking care off off siting of backups).
SnapMirror will copy the snapshotted volume(s) and all snapshots will also be mirrored. So 'snapshot1' on the source vol will also exist on the destination volume. VSC can also update the mirror as part of the backup, by the way.
4. Finally deduplication of data. If I take a snapshit using SMVI can the array then subsequently provide deduplication?
Yes, dedupe is effectively independant of the snapshots.
Hope this helps,