As for the JME topic, I still think that logically something destroyed in the past won't exist in the future and so destroying it would have been a better thing to do.
Like I said though, even if you follow that theory (that you can change the past etc.) then this won't be good enough. If the JME were destroyed in Squall's time but reinvented just one day before Ultimecia decided she needed to get to the past, that would have been enough to allow Ultimecia to get hold of the machine.