I saw a passenger next to me texting at 37k feet over Kansas on an JFK-SFO flight once. It was SMS, not iMessage (the message bubbles were green). How did he get signal up there?
He's probably got better signal there than I do down here on the ground. Cell towers have a range of about 5km at the absolute minimum, and a whole lot more than that if there's no hills in the way (e.g., if the phone is directly above them).
Actually directional antennas make no difference in regard to their allowed transmission power. The allowed power is specified as EIRP (Equivalent isotropically radiated power), which specifies the power a perfectly isotropic antenna emits. So if you increase the gain of your antenna, you have to decrease the amount of power you feed into your antenna to stay inside legal bounds (assuming of course you were at the maximum allowed transmission power to begin with).
What you do gain however is gain on the receive path (so you can hear the mobile phones better). Also the possibility to build segments and thus increase the usage of your frequency bands.
Yes, in densely populated areas with high frequencies (3G/LTE). In more rural areas the antennas cover a bigger area. My experience in light aircraft (operating below 10000 feet) is that 2G GSM connectivity is pretty good, 3G not so much.
