It depends on the device, did this computer come with W7 already on it when you bought it new? If so the W7 product key may be built-in and pre-activated. If not then if the W7 key is on a sticker on the bottom of the machine then that will work too, Otherwise, if you can't find your product key then I'm afraid you are correct, you will have to buy a new one.
When you install W7 over XP it is a custom install, not really an upgrade, so only programs installed by W7 will work (calculator, notepad, etc). All your XP programs must be reinstalled fresh.
And yes W7 has additional security so you don't have ownership of any old files/folders, those are assigned to the system "administrator", you are just AN "administrator" but not THE administrator. If you need access to data, etc, as an administrator you can "take ownership" of it, but the system is designed so normally you only have access to data stored under your specific user libraries. Example for me all my libraries are under C:\users\TrainableMan and in those I do have ownership.