Installing OS X on external hard drive, and installing from external HD

Maybe. If you have a universal OSX 10.4.x full retail installer disc,
and attach the iBook via Firewire to the desktop computer, it may
work and the iBook could be seen as an extra drive to the desk Mac.

You can choose where to install the system, but you probably couldn't
use a computer-specific installer disc when trying to do this between
dissimilar computer architectures, models or series.

There are bound to be details and quirky steps before getting things to
work; and ideally you would have an external optical drive (FW) and
use it to install a new system to the iBook. ~ And get it fixed, too.

...can i use another mac to install OS X on my external hard drive, and then install the OS from the external hard drive back to my ibook?

That is not possible.

You could (1) install OS X on an external FireWire hard drive, (2) boot your iBook from the hard drive, (3) clone the OS X from the external hard drive to your iBook.

Thank you for clarifying the limited but adequate option in this situation;
I have an external hard disk drive of FireWire enclosed type, and use it
to make full computer drive clones all the time. Just in case. 🙂

Use an application such as SuperDuper.

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There are a few fairly good clone utilities available; although I use a
donationware (runs uninhibited direct from download online) by Mike
Bombich named Carbon Copy Cloner, with a good amount of inform-
ation available at the home and download pages for reference; users
have had good use of Super Duper, CloneX, to do backups & clones.
Other utilities, such as the Disk Utility in your system install/boot disc
can be used to move a bootable archive of your system between disks.

Drive Genius (a retail software product) is said to be able to utilize
clones, but I have no experience in that product; although I do own it.
I like Carbon Copy Cloner, and test my clone's ability to run the Mac
before attempting to zero-reformat the machine's internal hard drive, etc.

A simple search of Mac sites (I use google.com/mac) can bring up
discussions specific to these third-party tools. The home page of
Mike Bombich's Carbon Copy Cloner is worth a detailed look into.
OS specific versions are available. http://www.bombich.com/software/ccc.html

With a compatible Mac OS X installation package and a drive connected through FireWire, insert the disk into your computer and follow the onscreen instructions; in the case of multiple disks, start with the first one. If there is no OS installed on the computer, press the C key after inserting the disk and restarting the computer. You can also clone the OS as documented above.

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