Those early Intel iMacs have a pretty much identical layout to the G5 units, so that guide should work just fine for your Mum's iMac.
I have no idea why you are having problems with iTunes and Flash, what OS is it running? Snow Leopard only costs £25, so definitely worth upgrading if you haven't already as that should fix any issues like this. My Mac Mini is of a similar vintage and I have not had any of the problems you describe. As for communicating with the network in your house I fail to see why this is an issue, I can access my NAS from my Mac via SMB just as easily as I can via Windows or Linux??
A "normal" machine would not necessarily have drives formatted as NTFS, they might be FAT, or they might be EXT2 or EXT3 depending on the operating system (Windows or Linux). The only reason you need a bit of software for your PC to read the drive is because Windows does not ship with the ability to read multiple drive formats, only NTFS and FAT. So, you would have to do the same thing even if it was a standard Dell PC running Linux - In other words, this is not a Mac specific issue.