Yes, you can backup your data by copying the whole folders from one drive to the second ( or external)drive. I do this when people bring me computers that are somewhat borked and need the OS to be reinstalled to work properly. I right click on my computer, then click explore to open up a double pane window. It is thru this window that i drag and drop whole folders to a second hard drive. It takes some minutes to copy large folders but its the easist method i know of. Copy and Paste does the same thing, just a couple more steps to the process is added because you have to go up and click on copy and then open up the other drive and go up and click paste.
Like you, i have had some problems installing XP as a upgrade to a older system on some computers. That is why i suggest doing a backup of any data you want to save and then do a clean install of XP. A clean install will give you the best computer with the least amount of problems. Adding a external HD later will give you your data back to the computer. Yes, i would remove the second HD before you install XP.
If you are going to clean install XP you might as well just format the drive as NTFS and be done with it. XP will still see the FAT32 external drive and you will still be able to access the files on it. Later you can convert that drive to NTFS also in computer management in XP.