The drive needs to be formatted as Mac OS Extended for use with FCE.
I would not (ever) advise using the same drive for backup that you are using for live data. 1) it negates the whole idea of backup (live data + backup on the same drive) and 2) Time Machine will interfere with video data streaming from the other partition on the same drive.
Buy two drives. Reserve one for live data (video editing, photos, etc) and the second drive for backup. But both FCE and TM require Mac OS Extended format. If you need to use the drive with a Windows pc, I suggest installing MacDrive software on your pc.
May I recommend G-Technology G-Drives and OWC Mercury Elite Pro drives. I have never been a fan of the WD MyBook drives; they are consumer-oriented, you have to watch out for the specs and they have had a less than stellar record when used with Macs.