Is it possible to determine the approximate climb rate of an aircraft knowing its top speed, engine power and weight?
Yes, but the process will be indirect. For a rough estimate, the engine power- which is the rate at which it can perform work- can be thought of as lifting the mass of the aircraft upwards against gravity. Since the units of power are foot-pounds per second and velocity is in feet per second, the engine power and the aircraft's mass can be used to solve for the climb rate in feet per second (be sure to use the right units for mass). this ignores airframe drag and propeller efficiency losses and as such yields an absolute upper limit for the maximum possible rate of climb. Your mileage will be lower!

Note that engine power depends on density altitude, and hence this estimate holds only for the density altitude at which the engine's power rating was measured &amp; specified.