Yes- fixing the MBR does not require a license
Yes- the product key is the license not the cd.(but you're not allowed to make copies)You will find that you need to be explicit with the XP version as well as which service pack is installed. Also that OEM versions (HP,DELL,Emachine) etc) will not work with a retail XP cd and a OEM product key.
There are many programs on the UBCD that can be used for diagnosing. It's one of the best.
UBCD4Win is another that is good.
GetDataBack--> recovery tool
Memtest -->ram( is included in both UBCD and UBCD4Win)
Knoppix--> A linux based bootable live cd that can enumerate hardware in its startup and show errors if a problem arises, or, if it runs perfectly, then it shows that its more likely a software issue rather than hardware.
In all, experience is the best tool, and EE is probably the best tool you can use as the experts here have a wealth of knowlecge to share.