Try a test. With the computer booted up, plug in the USB drive. You should see an entry added to /etc/mtab with identifies the device and the mount point (probably in /mnt or /media).
Then, in your file manager, look in /mnt (or /media). If you see the USB drive listed, then there is no reason why you can't install Ubuntu to the drive. Just be sure that you install the bootloader to the MBR of the USB drive and not to the internal hard drive.
Then, reboot and enter the BIOS setup of your computer. Verify that you can set the boot order to poll the USB drive before the hard drive in search of a bootable OS. If your BIOS supports USB boot, then you should be able to boot from USB as well as internal drive.
but the fact is that i heard his HDD supports only FAT32 filesystems
This basically means that the vendor has drivers and admin software for windows systems and not Linux. It does not mean that the drive will not work on Linux systems. I find Linux USB support to be well developed. I haven't had any problems using several types of USB hardware, inclucing hard drives.