You shouldn't back up SQL Server databases from the filesystem level, it should be done by taking SQL backups and then backing up the SQL backup files.
To remove the locks from the files you either have to stop SQL Server, take the database offline, or detach the database.
If you want to replicate SQL Server databases you really should investigate one of the replication techniques within SQL Server itself. Using DFS-R you're more likely to corrupt your databases than anything else. That said, be careful what you wish for. It can easily take an entire full-time dba team to support SQL Server replication.