Yes the phone also transmits back to the tower.
In GSM the phone transmitter maximum power is 33 dBm. In LTE the phone transmitter maximum power is 23 dBm. The transmitter power is smaller, when the phone is closer to the base station, as it smaller amount of power is sufficient for reliable communication.
Below is a simplification, but I believe it matches your current knowledge on the subject.
Imagine you had an isotropical antenna (which actually is physically impossible, but bear with me). An isotropical antenna transmits the RF energy spherically. Assume you are transmitting 1 W of power. The 1 W power now divides evenly to the surface area of the sphere. However, the surface are of the sphere depends on the distance.
Assume we are 10 meters from the transmitting isotropical antenna. The surface area of the sphere will be:
\ A = 4*pi*r^2 = 1257m^2,
The transmitted power is divided evenly to the sphere area. Thus, the power density is
\ Power density = 1 W / 1257 m^2 = 795 uW/m^2,
If we are a hundred meters away, the area of the sphere is 125714 m^2. So the power density is
\ Power density = 1 W / 125714 m^2 = 7.95 uW/m^2,
So you see, the further you are from the transmitting antenna, the smaller the power density (or field strength).
Yes, LTE (and GSM) transmits with a greater power when the connection gets worse.