I want to know what it the lowest tire pressure you could put on a maximum rate 44psi tire? I have been placing 33- 34 psi on these tires for about half a year now, will it damage my tires? I'm planning to put 36psi to it to make it near the rated maximum limit.
Tire pressure is typically determined by vehicle weight and type of tire. In other words, the 44 psi you refer to is the maximum inflation of the the tire at its maximum load rating.
You can safely inflate the tires to the maximum pressure, but it may not give you the best ride or performance. Each vehicle has a specified pressure/load rating on a placard in the door jam area. It may look something like this;
Since you've not given us information about the type of tire or the vehicle, I will say to use a pressure 10% to 15% under the maximum psi rating to get the best performance of the tire.
This is just a guess and you will have to do a little research yourself depending on the brand tire and type of vehicle.