Generally speaking external drives don't have the throughput to run software as quickly as you would run it from your laptop's internal drive. That said, many so called "portable" versions of applications do exist which can be run from external drives; PortableApps is the best resource. Running Firefox in this way for example lets you keep all your bookmarks and preferences from machine to machine.
Personally, I'd advise not partitioning external drives with multiple partitions. From experience I'd always "eject" one of the partitions and forget to eject the other before physically unplugging the unit, which can cause data loss. If you're less absent minded than me though, fire away :)
Your primary concern would probably be be which file system to use, and it largely depends on the machines you'll be using it with. Provided you'll be using it with Windows XP, Vista and 7 computers, you can get away with just using one partition and NTFS for maximum reliability and performance.
Partitioning tools exist in Windows 2000 and later under Administrative Tools → Computer Management → Storage → Disk Management. If this doesn't work (rare, but not not unheard of), PartedMagic is a free, bootable Linux distribution with very simple to use graphical partitioning tools. As with any hard drive operations though, remember to back up your data before attempting anything!