Hi Felix,
Yes, if multiple VDBs are assigned to the same SQL Server instance on a target, they would have to be named uniquely.
LogSync works exactly as you suggest.
Delphix keeps track of the transaction log backups as they happen on the production source and takes a snapshot after restoring each one on the staging server. If LogSync is enabled, the transaction logs are preserved. When provisioning, we pick the closest snapshot to the point in time that you pick, and then apply the transaction log (using the "stop at" clause).
Hope this answers your questions.
-Ankur