Do I have to partition the drive and format the new partition as NTFS to use it for windows files?
NO, but it will have to be FAT32 .. not Apple HFS format. Windows can read/write FAT32 and OSX can read/write FAT32 .. this is the best format to allow the HD to be usable by both OSes.
My disk has the Mac OS Extended (Journalled) format at present.
Then you'll need to reformat the entire drive or split into 2 partitions and format the Windows one as FAT32 or if you want it for Windows alone you can format it as NTFS (but only when it is opend from within Parallels).
Also, I usually eject the disk at present before opening Parallels as otherwise, I think, I get the Device Removal error. How do I connect to the drive when I am in windows?
Wait until parallels is up and running, then plug in the USB drive .. Parallels should then ask you if you want the USB drive available for OSX or Parallels.