What is so special about Egg 00 as opposed to every other egg?
Egg 00 is probably the current loaded egg. Maybe the eggs are moved from position to position through some means. The Egg 00 room was probably created for hatching. Perhaps Egg 00 was the only egg still able to be hatched properly? Not enough information to do anything but guess...
Why would Kazuma only be able to gain access?
Hacking the password on the egg's hatching process.
Neither was ever truly explained. Couldn't they just hatch another Dragon and get off the island that way?
There was only one dragon that didn't attack on sight. The only dragon that was also safe to ride immediately after hatching.
That can't just be a coincidence that the "ready" egg, was the only safe egg which was used.
The sisters could clearly fly. Or were they simply not aware of any other egg, or like Quote, could not gain access?
There were definitely other dragons ready to fly... But, like previously mentioned, perhaps the only proper way to hatch an egg was using the Egg 00 chamber? After all, that chamber had direct access to the outside, while inside the corridor would probably be a dangerous place to hatch a dragon. If one got loose... who knows what kind of damage it could do to the corridor.... It might be a more sensitive system then we believed...
How do you password-protect an egg anyway?
That's probably just the hatching process? The only way to activate the system and have it hatch properly, requires credentials. And just cracking an egg open might not be a good idea...
Why was it protected by a force field?
If it was indeed a hatching area, then perhaps that area would be better protected, to keep a young dragon from escaping and damaging the corridor. That large area before the Egg 00 chamber might have been used to interact with young dragons...
Would there be a matching force field on the outer wall?
There wasn't one in-game, so I'd imagine not? But, there must be some way for the Dragons to fit through the door; perhaps through hidden gate, and if the eggs can be moved from location to location to the hatching area of Egg 00, then they too would need a system that moves them.
Why was the force field controlled by a computer and keycard in two empty eggs of all things?
It seems Igor was the one looking after the lab after the loss or disappearence of the professor running that hatchery. Igor apparently had a source of red flowers, and perhaps red flowers were being used in some fashion with the dragons. After all, the failed hatched dragons, were called Zombie Dragons...
Anyway, the keycard was probably put in the eggs for safe keeping by Igor. He seemed... somewhat sane... and somewhat insane...
It's not a bad hiding spot too... He was the most sane frenzied Mimiga we were able to meet, maybe the PC too was put there...
What happened to the Dragons from those eggs?
Perhaps they failed to mature and were disposed of, or... perhaps the false egg was a trick the professor came up with to hide the items needed to take control of the corridor.