Assuming that you have NTFS partitions and not FAT partitions then you are advised not to try to write to them in Knoppix. As for saving data some people use small flash drives with FAT partitions, other create a small FAT partition on the drive for this purpose.

Sure, you're absolutely correct that Lnix will run faster from hard disk than CD. It will run even faster from RAM, so if you have a gig or more you might want to boot the Knoppix CD with the toram cheat code. You're not on the right track if you want to "install" Knoppix to the hard drive though, that opens a whole can of worms. If you like Knoppix consider installing Debian Etch to hard disk. Knoppix is made from Debian so you can do everything (and a lot lot more) with Debian that you can do with Knoppix.