http://db.tidbits.com/article/08405
Won't work. You can not select external drive to mount OSX 10.5 and above to
I think you may be confusing some things -- or I am confused.
Anyhow, when Apple transitioned from the PPC platform to the Intel platform, there were some hardware changes that resulted in different partitioning.
PPC --> APM
Intel --> GUID
If you partition your external HD with GUID, then install OS X on it, you can use it to boot your Mac. In fact, I do it with Snow Leopard and my MBP15. Internally I run Tiger. But when I want to run SL, I just boot to my external FW HHD.
However, I cannot use the same external FW HDD to boot my PB15 since it has the GUID partition system. I must repartition to the APM partition system. Because of the partition system difference, it creates the impression that you can't boot from an external FW HDD ... but you can.
Trying to get my computer to work, with a blown internal hard drive using the LaCaie FW drive, until I have the time to open my mini and replace the hard drive which is dead and processor which needs a speed boost
Do you have the install DVD's for the Mac Mini?
If so, all you need to do, is boot from the Install DVD, then run Disk Utilities and partition your external LaCie FW drive as GUID, then format the HDD as Mac OS Extended (Journaled).
Then install Leopard on the external HDD.
When you are done, you might be able to use Disk Utilities on the external HDD to recover the internal HDD on your Mac Mini -- at least to the point of saving/recovering your data files. You also have the option of installing other good recovery programs for Mac OS X to use on your internal HDD.
On a side note, I see where you are trying to mount then recover using a DMG of the OS. If I may, I would suggest cloning using Carbon Copy Cloner or Super Duper on a weekly basis to alternating external HDDs. That way, when your internal HHD dies in the future, you can merely boot to the cloned backup. Much simpler that way, and easier to do. Plus it puts you back in business in a matter of seconds. And if you also use Time Machine to another external HDD, you will have all your latest data files available to you.
Hope this helps. YMMV.