You can start at the handle or the screw extension and work from either end.
Starting at the handle, treat it like a beam and apply say 1 pounds of force. This results in loads on the fulcrum and the plunger.
With the load on the plunger, use the diameter to get a pressure apply the pressure to the bottom of the ram. calculate the force on the bottom of the ram.
At one pound on the handle the ram pressure will probably be less than the rated capacity of the jack. So proportion the jack capacity to your result and increase the force on the handle and all of the resulting stresses and pressure by that amount.
Use your new pressure to calculate the stress on the outer cylinder walls and ends.
The screw threads are in shear.