Connect the TV to the same router. A hard-wired connection would be best, either ethernet or a power-line network interface. A WiFi connection probably will be OK if there isn't too much RFI. If you run a DLNA service on your Synology NAS, then, in principle, that should be all you need. The TV should see the DLNA server and let you browse through the available movies.
1) The movie files (container formats, video formats and audio formats) have to be in formats that the TV's DLNA client recognizes. Check its manual for details.
2) They might be subject to Cinavia copy protection depending the movie and on the client software implementation in the TV.