[Wickers]

1: Does Apple sell re-furbished logic boards?

Short answer, no, Apple does not 'sell' refurbished iBook G3 logic boards to people who have the logic board replaced under the replacement program.

The replacement program covers the part and labour for a logic board replacement on G3 iBooks if the iBook is showing the right problems. (mostly video related.)

Guess what, most of these boards were made back in 2001... now, the 'Apple 2001' thing you saw might just be the date of design too. Either case, if you replaced the logic board through the program, then it does not matter what logic board Apple gives you, as long as it works.

2: Anybody ever had problems powering their laptop on an airplane?

This could have been what caused the relaps of the iBook... but it could also be many other things.

3: Is it possible or likely that the constant rebooting between OS9 and OSX
is what's causing the logic boards to fail?

I don't see any reason how booting into OS 9 and OSX back and forth would cause problems... in fact that sounds a bit odd. Now, what could cause a problem is if you are in OS9 and you start poking about your OSX folder. . . this may fuck something up.