Is it possible to partition external hard drive into 2 partition and put Ubuntu live image on one of the partitions? And how can I boot from this partition?
Sorry for slow response.
I am actually running my Ubuntu installation this way. You need to perform the installation with but a few changes:
Follow How do I install Ubuntu? up to the "Installation Type" prompt. Here, you must select "Something Else".
Find your external hard disk in the partition list, and click its partition. Click Edit. Change the size to leave some empty room, removing at least 20000 MB as a bare minimum(I recommend at least 100000MB).
Click OK, and allow it to apply changes. Now, click in the free space created, and click Add. Add an
On the bottom, click in the dropdown for bootloader installation, and select your external hard disk.
Ensure that it isn't your internal hard disk!
Click install, and continue with the instructions.
To boot, ensure your hard disk is plugged in, and press the key for the boot menu(usually F10, esc, or F12), and select your hard disk to boot from, and proceed booting as normal.