Questions 3 and 4 are defective because the Absolute Ceiling and the Service Ceiling are two different things.
RATE OF CLIMB
Best attainable rate of climb is equal to excess power divided by weight. Excess power is equal to power available minus power required. As altitude increases, the power available decreases and the power required increases. This means that as altitude increases, both the excess power and the maximum available rate of climb gradually decrease.
The Service Ceiling is the altitude at which the best attainable rate of climb has decreased to certain specified values. These values are 100 ft/min for propeller aircraft and 500 ft/min for jet aircraft.
If the aircraft continues to climb above the service ceiling the power available, excess power and best rate of climb all continue to decrease. The absolute ceiling is the altitude at which power available is just equal to power required. At this altitude, the excess power and rate of climb are both zero.
Both power available and power required vary in proportion to a number of factors including weight, load factor, altitude and airspeed. For all powered aircraft there is a speed at which the excess power and hence rate of climb are a maximum. This speed is called VY.
ANGLE OF CLIMB
The angle of climb of an aircraft is proportional to the excess thrust divided by the weight. Excess thrust is equal to thrust available minus drag. As altitude increases, the thrusts available decreases. This means that as altitude increases, both the excess thrust and the best angle of climb decrease. At the absolute ceiling the thrust available is just equal to the drag and so the excess thrust and the best angle of climb are both zero.
As airspeed changes, both the excess thrust and maximum climb angle change. The maximum climb angle at any given weight therefore depends upon the airspeed. The term VX refers to the calibrated airspeed at which an aircraft can achieve the greatest angle of climb.
At the absolute ceiling the thrust available curve is tangential to the drag curve. This means that there is just one airspeed (VX) at which there is sufficient thrust to maintain altitude and airspeed. At any other airspeed the aircraft will have insufficient thrust to maintain altitude, so it will descend. At this altitude the power available curve is tangential to the power required curve. This means that there is just one airspeed (VY) at which there is sufficient power available to maintain airspeed and altitude. At any other airspeed the aircraft will have insufficient power to maintain altitude, so it will descend. Both of these conditions occur simultaneously, so at the absolute ceiling VX is equal to VY and the best angle of climb and best rate of climb are both zero.