If you want everything works properly, then the answer is yes. Note: Yes
There is no "DOS mode" for a hard drive, and it is not necessary to use DOS to format a hard drive. Vista's installer had a built-in partitioner and formatter.
Yes. Actually, there is no need to remove the hard drive. You can format the existing hard drive and install XP on it as well. Note: Yes, you can there is no need to remove the hard drive. You can format the existing hard drive and install XP. and also you can install both opreting system single computer. XP and vista both.
Format and reinstall.
You'd need to boot from some other drive and then use a utility to format the hard drive. One that you can get for free is called DBAN ("Darik's Boot and Nuke"), which will not only format the drive but completely erase everything that's on it. You'd then need to get some other installation media to install a new OS on the hard drive.
There's no such thing as Windows XP format or Windows Vista format. You should check however if your external hard drive uses an NTFS or FAT32 partition table. You can see that by right-clicking the drive (C, D, E, ..) and clicking properties. If it uses NTFS it will be no problem for Vista. If it's FAT32, then google for a way to convert it to NTFS. No big deal.
If you are trying to install xp, you have format the hard drive prior installation. If you trying to reinstall Vista, check your hard drive for bad sectors. Make sure that the installation CD/DVD is readable (just try to copy all content on your hard drive).
The Vista tool used to encrypt an entire hard drive is BitLocker Encryption.
There is no such thing as not being able, in most cases people have no idea what they are talking about. Vista uses a special "protection". As result if you want to install xp on the vista partition it will not allow you do so. There are some steps which must be taken if you want to format vista partitions.
Windows Vista does not officially support booting from a FAT32 drive, although it is technically possible. Vista supports FAT32 on Flash drives and hard drives, although it will not format a hard drive over 32 GB as FAT32.
When you reformat a hard drive you change it to whatever formatting you have selected and it will overwrite whatever format was used before.
No. Vista ruins all windows(non-vista) and RAIDed partitions.
Sounds like a problem with Windows XP. What you should have tried to do is take the original hard drive, put in the xp install disk, to the install, choose to format the hard drive, and then continue with the XP install. BTW: XP > Vista. Linux > XP. You should install Linux, instead of XP.