Here is my question- Can I install Ubuntu of a partition of a portable hard drive? Hard drive in question is this one. I want to give it half the total size available and also want to know if the OS will be portable and hence if I can run it on different systems.
In theory yes, assuming the system is the right architecture - you will need to set up the drive to be bootable (which many drives are anyway - you would see these drives as a fixed disk under windows ), and simply install ubuntu to that drive. Assuming you don't try to run 64 bit ubuntu on a 32 bit system (so its safer to use the 32 bit system), the worst that should happen is you would need to boot into safe mode. I used to do it with a bunch of 32 bit systems, but they were all the same generation/design of 32 bit x86 (I was running mostly core 2 duos).
I'd recommend a less 'heavy' varient of ubuntu, since they don't rely as much on compositing. Linux handles switches of hardware surprisingly gracefully, unless it lacks a driver you need, and the basic install includes a lot of things you 'might' but don't always need.
I'd also recommend doing the install of linux to the external hard drige on a system with no other hard drive on it to ensure that the bootloader is installed to the MBR of the external drive. This isn't necessary but makes things more foolproof.
Finally your mileage may vary - some systems simply do not boot off some external drives, and you will want to test this arrangement on a few systems before trusting it to be your daily driver system.