There are free tools available for all of this, but choosing the right tool may be a bit difficult.
The easiest way to backup files is with a backup utility - 2 highly recommended one's are SyncBackSE and Cobian (do a Google search for them)
The easiest way to backup the operating system and programs is with a disk imaging utility (but I can't recommend any free one's as I use Acronis True Image (costs about $50 US)). This will preserve the hard drive in the state that it exists when the image is made.
There's 2 primary reasons for not using imaging software to do backups. They are:
1) The size of the image is huge and contains everything whether you need it or not
2) Exploring the image to retrieve info stored there isn't very easy when compared with backup utilities.
Also, while you can backup programs and the OS using a backup utility - restoring it will be durned near impossible because:
1) Installation programs hide entries all over your hard drive and in your registry.
2) Windows Security Identifiers/permissions/access lists may not allow these programs to function even if you successfully copy/move everything around.
I don't think that you'll need to partition the new, external drive unless you want to do it to keep things neat. Otherwise, just make sure that you've got a good plan for how to organize the files on the new drive and you'll be ready to go.
Why your E: drive contains those Microsoft programs? I dunno, but would suspect at one time or another the installer for them was pointed to the E: drive and it has remained that way.
Converting to NTFS is a good idea. IMO it's a more robust and forgiving file system, and it has extra security features that FAT32 doesn't have. That being said - if it ain't broke, don't fix it. If you're not having problems, then why try and remedy it? (FWIW - I've never listened to that sort of advice!
Seriously, if you've got a good backup and are in the mood for some experimentation, first try restoring the image of your OS to the hard drive to see if it works. That's the final test of any backup/image - trying it to make sure that it works before you need it! Once you're assured that the image restore has worked, then try to convert the partition to NTFS. If it crashes, then you can restore the image without any problems (since you'd already tested it and it worked then).