Cell phone tower operation

Pardon my ignorance if this is simply stated in wikipedia although I thought to ask here, So I am wondering how does exactly a radio tower communicate with a cell phone? Yes obviously by radio waves in the microwave? or so about region, but ok let me try to ask this in stages, 1)The radio tower is supplied by a power cable from the nearest power line because the antennas and the RF amplifiers and other apparatus need quite some power in order to radiate the radio frequency signal, I can understand that, similar with tv broadcast tower antennas and other, now this signal is then transmitted in a certain radius around the tower, the length of which is probably proportional to the power of the transmitter in the tower, after certain length the signal probably becomes too weak to be distinguishable from "background noise" so another tower is needed and they are linked as much as I know by their own antennas in order to transmit signals from tower to tower. Now ok say I have a cell phone and I am in the zone where signal strength is good and my cell phone picks up the signals and so I see whose calling me and can hear him etc, but how does my phone sends my voice/message back to the tower? Yes I realize by the same radio frequency (microwave region?) but how can the tower detect that weak signal coming from my phone because unlike the tower my phone has a small 3.7 volt tiny battery, I wonder how can such small amount of power be enough to create a radiowave strong enough to travel miles and then be picked up by the tower? 2)What is the major difference between the towers transmitter antennas and receiver ones? because the signal from my cell phone is probably very weak so if I am in countryside and my nearest tower is many miles the receiver antenna needs to be very sensitive in order to get my signal? What happens if there is some "background noise" around the frequency in which my signal is transmitted? 3) the third question for now would be, what kind of encoding cell phone transmission exactly uses? I know how AM and FM works but haven't really read upon or know how all this digital tv transmission works or cell phone apart from the basic physics of how radiowaves and carrier waves etc work, so can someone please say something about that ?