what happens if I play offline on my mobile phone?

Mel-3

for example, when I'm in an airplane and play King games offline and I would pass a level - does this synchronize as soon I have internet access again after landing?

Tune_D

Hi Mel, just in case you're about to take a flight and wondering whether or not to play; yes it does! 

You can easily connect afterwards to your Kingdom account of your Facebook and it will synchronize your progress ;-)