Stock Dell cpu heatsink fell off (some basic questions)

Well, my parents had been having problems with their Dell desktop shutting down at varying intervals after startup. After starting it up a few times myself, I found that the interval to shutdown was considerably shorter immediately after a previous shutdown; so, I assumed it might be a thermal issue. So, I opened it up to find that the cpu's heatsink was loose and now I have some questions reguarding reattaching it.

First, the plastic frame that is attaced to the motherboard and which the heatsink is clipped to is broken. Do I need to order a replacement from Dell? Would an aftermarket cooler require this same attachment to clip to or would it come with its own method of attachment?

Second, looking at the surface of the heatsink that is normally adhered to the processor, I see a square piece of thin metal adhered to the larger block of the heatsink with a black compound. The surface of this metal is deeply scratched in several places. Am I correct in assuming that this small metal piece is what I should clean and affix to the surface of the cpu using thermal paste? Are these scratches an issue?

I appreciate the help. BTW, I do have some alcohol to clean it and some arctic silver 5 to reattach it.

Actually, it's a pentium 4. After doing some more research, it turns out that this is a common problem with the Dell dimension 2350. The heatsink retention bracket breaks leading to the CPU overheating. I've found new brackets for sale online, but I'm going to see if Dell will take care of it considering how many people are having a similar problem.

Thanks for the help. I think I've got it covered from here.