Not sure if this is possible.

The Panasonic DVC camcorder has firewire and USB connections. The monitor has DVI and VGA connectors.

Am I correct in thinking I should be able to play back directly by connecting the firewire camcorder outlet to the DVI input connector of the monitor?

Sorry but no, firewire (IEE1364) and DVI are not the same or interconnectable. This is why firewire to DVI cables don't exist!!

best suggestion I could think of was to copy the movie files over via usb or firewire then playing the files back via a media player

Depending upon software and hardware you might be able to just watch your recordings via your PC without copying or editing them first.