Adaptive vs. Static security model in ABE
Towards Q1 -- immediately should just mean that the adversary has no more information as the public parameters (so it doesn't have to be "few seconds" but. "without any intermediate messages")

Towards Q2 -- assume you have some system with a weakness like the following: If you get to send an valid encryption to the challenger, the challenger responds with the master key. You won't be able to exploit that in the static model (with overwhelming probability) but in the adaptive case it's easy