Apple's Software Restore is actually a CD that ships with any Mac you buy. It'll restore your hard drive to the original state that it shipped in, meaning it wipes your hard drive clean and re-installs all the software that originally came on the HD with your Mac.
I don't think there's a way to install OS X from a hard drive. I believe you HAVE to boot up from the OS X Install CD and install from there.
No, you CAN install from the HD, but then you need a free extra partition. It's easy; find the Apple Software Restore application (only the app), an copy it to your HD. Then drag the 10.1 install CD onto the ASR icon, and do the setup, and select it to "restore" to the free partition.
Then you can boot from the HD, just as the installer CD