I found this question and it is very similar to my situation. I am satisfied with zkriesse's answer but I want to know whether data in my external hard disk would be lost using this method. And what about Fernhill Linux Project's method ?
Also, I downloaded the Universal USB Installer and thought of directly installing Ubuntu to drive J: (which is my external hard disk) but for that, I had to check "Now Showing All Drives (BE CAREFUL)". Would anything go wrong if I go ahead ? Why does it say, "BE CAREFUL". Would anything go wrong if I install ubuntu into drive J: directly without checking the "Format J:\ Drive (Erases Content)" checkbox ? I repeat that I CANNOT AFFORD TO LOSE A SINGLE BYTE OF MY DATA IN THE EXTERNAL HARD DISK.
Partition your HDD (resize and then Create New Partition out of free space) Then Install everything to that Partition. You can make two partition one for /home and another for /
That is the safest way I can think of and if you do it careful enough (that you do not mistaken your HDD for the one with data) you are 100% sure that your data is untouched
On Second part of your Question, do not use Installer. Its purpose is to make bootable stick for thos who cant install Ubuntu with CD/DVD. Though you can have it with persistence, but its the Worst idea! Just do normal installation!