OK, some answers, although they may not be the questions you need answered now:
On the original install, which completed and gave you the original flashing question mark - not using the second CD may only be because you used a Custom Install and didn't install all those other languages and printer drivers you were never going to use.
When I re-format and re-install OSX 10.2.0 from the discs that came with my MDD G4, I cut down on the install too, no printer drivers, no foreign lanhuages, no software packages that I'll never use, like IE and iMovie. Disc 2 was never used, everything I needed was on disc 1.
One simple cause of the flashing question mark is that the PRAM battery is dead. This would maybe lead to a scrambled PRAM when you first attached power. So those that suggested resetting PRAM were correct, it helps get some order back to the Mac, but as it stores the startup disk also, with a dead battery it's never going to be correctlly held. A dead PRAM battery results in the flashing question mark on the old G3 towers and G4 towers, but I haven't read of it causing this on a PowerBook / iBook, maybe because they have only the one disk, but it could be the cause of your first issue. Then my 17" Aluminium PBG4 has a dead PRAM battery and it has no issue booting from the internal disk, maybe I've just been lucky.
Burning copies of the original media doesn't help you. I've found when I tried to make copies of the original install media for an old iMac G4 (OS X 10.1.4) using Toast Titanium, they were useless. If I imaged the discs as CD-R / DVD-R Master in Disk Copy / Disk Utility and then burned them to discs in Disk Copy / Disk Utility they were fine. Almost all my original bootable / install media since have been the same, I had to use Disk Utility to copy them. Think it has something to do with the Partition Map used on the optical media, Toast just gets it wrong.
I'm beginning to suspect that the "The Installer has quit due to an unexpected error. (exit code 0) Please restart your computer." is a red herring, it would appear to only surface when you're trying to install OSX 10.2.1 on top of an OS already installed. If you'd been able to boot after the original install it would not be an issue. I have seen that error happen before, but only in later Mac OS's, ie. OS X 10.4 and 10.5, when the Mac OS gets very fussy about the quality of RAM - which is why almost everyone asked you to remove the extra RAM or run a Apple Hardware Test. It doesn't really test the RAM thouroughly enough, it's usually only some third-party memory testing software for OSX 10.4 and above that does this. As you're trying to install OSX 10.2.1 Jaguar, and it's not too fussy about the RAM, it shouldn't be the issue, but we could be wrong. Just checked the iBook specs, it uses PC-100 RAM, and I've only seen it before where the Mac required PC-133 RAM and the RAM installed identified itself as PC-100, so again, shouldn't be the issue. If you can run the Apple System Profiler while booted from the install disc - don't know, never tried it, or even looked to see if it was available - then that would be a good check. Also make sure that it reports the RAM sticks as the size you expect them to be - I've seen suspect 512MB RAM come back as 256MB or Empty in ASP, as well as being reported as lower speed.
