I am currently designing a solar tracking system. I have a motor rotating a cylindrical beam. Forces acting on the beam are located as follow:

Force one: acting on the top of the beam -solar panel (fixed on the beam)
Force two: acting on the bottom of the beam.-caster holder. (stand fix to the ground)

I need to know:
1) how to calculate the torque provided to the beam from the motor.
2) how to calculate forces acting on the beam from the panel and the caster stand.

I assume that although you call it a "beam" it's really a columhn - meaning it standes vertical and rotates about its axis, right?

1) The torque induiced onto the beam by the motor depends on the torque that the motior can produce. If what you really meant to ask is how much torque is required from the motor to turn the column, this depends on the mass and geometry of the solar panel and the column, friction forces in the mechanism, and the minimum spin or "slew rate" that you want the mechanism to be capable of.

2) The forces acting on the beam are (a) weight of the solar panel, (b) reaction force from the base countering the weight of the solar panel and the column, (c) dynamic forces due to wind, (d) torque from the motor to accelerate the rotation of the beam.