Your question is a pretty good one. With software, it's really not so much about physical media (disks) as it is about licensing. In fact, there are many ways to purchase or legally obtain Windows without getting a disk at all, such as via an MSDN subscription (where they do send you disks, but you can also download disk images from Microsoft).
Most computer repair technicians have a collection of Windows disks for various versions of Windows. Strictly speaking, they should verify you have a valid license before reloading Windows on your computer. However, in reality, most of these technicians are college students (or high school graduates) who are following a list of instructions and could really care less about whether you have a valid license or not. Also, most computers that are pre-loaded with Windows have a license certificate right on the box. So the tech can verify you have a valid license just by looking at that.
As for reloading your programs, they might not have to actually do that. You can do a Windows repair install that does not remove your programs. Generally, this is the "fix-all" employed by many repair technicians who are not confident in their repair skills. It is reasonably effective, but it doesn't solve every problem (especially hardware problems) and it could end up deleting your data and/or programs.
What you may not know is that deleting your data and programs is not a concern of most big-box store technicians. This is because when you give them your computer, you sign a form saying that you have backed up any important data and that they are not liable if they delete your data. Many people don't know this and are very surprised when 5 years worth of digital photos are deleted. So do keep that in mind.
As for buying an XP disk, I'm not sure what you're talking about. Do you mean getting one from Dell? Or is your technician charging you for one? Or are they making you buy another copy of XP?
The technician should be able to provide their own disk (especially if they feel justified in charging $100+ for an OS reinstall). However, if they require you have one, you can get one from Dell for like 10-15 bucks. Just call Dell and tell them you lost you Windows disk and you need a replacement. Then take that disk in whenever you go in for repairs. Or you can always do the repair install yourself. However, if you really have no experience in this, it's best to find someone experienced to help you out the first couple times.
Good luck!