Partitioning (the safest way):
Boot from the Panther installer CD/DVD. Run Disk Utility (from the Installer pull-down menu I think), select the drive (the manufacturer specific drive, not the current name of the drive (probably Macintosh HD)) you want to partition, a partition tab will appear on the right, select it, and the rest should be self-explanitory.
Caveats:
Partitioning this way will erase the drive.
Choose your partition sizes wisely. OS X needs AT LEAST 1.5GB of free disk space at all times to use as swap (virtual memory), so don't put yourself in a position where you will run out of disk space on your boot partition because of applications and the like installed.
Using a partition for "back up" is a Bad Idea™. If the hard drive fails, your "back up" goes with it. A partition is just a separation of 1 logical unit, if that unit fails, you've gained nothing.
To boot into target mode (this is what firewire mode is called), as you boot, hold down the t. That's it. Just t. There are a bajillion sites with many keyboard shortcuts for the OS. Here's a list of common ones, straight from the horse's mouth:
http://docs.info.apple.com/article.html?artnum=75459
If Safari is dragging ass, well it's possible that you are overloaded with favicons. Be sure to remove the contents of ~/Library/Safari/Icons/. This will remove all the favicons that you've likely accumulated.
If it's the comptuer running slower, I'd start with some normal troubleshooting steps, outlined here:
http://www.macosxhints.com/article.php?story=2004011205473937
As for 2 partitions, formatted differently for different systems:
http://www.macosxhints.com/article.php?story=20030613121738812