As for the cd rom drive not working while it is starting up to install windows could be because it would be a USB device. A USB device won't usually recieve power before accessing windows (or the installation) which is why you could be having troubles reading the disc, but not if it booted up the windows installation, as this would make it recieve power
I wouldn't know how to fix this.
as for the hard drive (as its removable and not inside the laptop (usb I'd guess?)) you could do that. Though if it was removable from the laptop and not using USB, I would not know how to do this I'm afraid unless it did still use IDE cables like a normal PC.
You could encounter some problems using Win xp though:
Windows XP has a protection feature where if it notices a big change in hardware, it'll stop windows working when it boots. In this case you would have a problem, though its worth a go.
Install it as you normally would in the desktop and then put it on the laptop. When it boots, you'll find loads of drivers that will be different which might make it fall because of how many they'll be compared to your other system.
If you wanted to sucessfully do this and have more of a chance, I would not install Windows XP onto it, but rather Windows 2000, or Linux if thats your thing (Though I don't know how well this would work), as it'll have much better chances of actually booting with the new hardware in your laptop and seeing the new devices
i have moved a hard drive from one PC to another and it has booted succesfully
Hope this helps, and works