Larry & Jim have pretty much answered your questions. As Larry says the virtual machine is simply one huge file when viewed in Mac Finder, (the equivalent of Windows File Explorer.) There are settings in Parallels to control Time Machine backups, there is a SmartGuard option that takes a scheduled snapshot of the Virtual Machine and helps to minimize the amount of data Time Machine backs up, I don’t use either.
A couple of Parallels Knowledge Base articles you might want to look at are: Backing up virtual machines with Time Machine - http://kb.parallels.com/en/8827 and "Optimize for Time Machine" backup option logic - http://kb.parallels.com/115052
I have my TMG backup files and TMG exhibits on the Mac side and they are included in Time Machine backups.
Larry and others have reported they don’t have problems with their TMG data on the Mac side, my MacBook is too old to run current version of Parallels so I cannot verify that; however it is relatively easy to use a data_paths.txt file and move TMG data to the Windows side if problems are encountered. See the Fixing a broken installation section in my Using TMG 8 on a Mac article.
A little research on EXFat seems to indicate that it should be OK.
I have a 500 Gb Maxtor Firewire Drive setup for Time Machine, it’s formatted Mac OS Extended (Case sensitive, Journaled), as a test I just created a folder outside the backup folder and using Parallels custom share folders was able to map that folder to a Windows drive letter, in Windows I was able to read and write a couple of test files. My other two external drives are NAS drives (Network Attached Storage, http://en.wikipedia....ttached_storage) I believe they have an embedded OS; I don’t know how their disk is formatted, they have their own IP addresses and are mounted like file servers. I’m guessing that if the Mac can see the drive you should be able to configure Parallels to map it or folders on it to a Windows drive letter regardless of the format.