Intermittent shutdowns doesn't sound like a hdd problem. More like a PSU problem. But I would wait for the problem to develop some more, as its most likely a hardware one, to be able to diagnose it more accurately. Plus it doesn't seem like a huge problem right now.
The hdd speeding up is probably because the information on the drive is so fragmented. So the computer is calling information up from the hdd, but its spread out over so many places that it has to spin fast and work real hard to find it all and pull it up, seemingly randomly. But in actuality its just program files that are being run that are fragmented throughout the drive.
She should defrag her hdd, which I'm going to assume she hasn't done since she bought the computer. Also to make sure that the intermittent shutdowns aren't a virus related problem; I would boot into safe mode and run a thorough virus and some spyware scans. Should also help clean up her computer even if there is nothing wrong with it.
She most certainly
DOES NOT need to replace the harddrive, however backing up important information is always a good idea
, I myself have a redundant drive.