Question

If we had two unknown masses on opposite sides of the pivot, could I calculate both masses given just the information used in the experiment?

Start with object A and place it at the 2m marker to the right of the pivot. Then move the slider to the right directly beneath the pivot. This will remove the pillars and you will see the balance tip to the right. 6. Now switch the objects back to the bricks and choose only 5kg mass bricks. Place as many as needed in whatever configuration that will balance the scale or put the system back into equilibrium. When the system is in equilibrium the leveling arrows will turn green. 7. Record the location of each 5kg brick and the location of the mystery object from the pivot. (Note: If the mystery object is too heavy or too light and does not balance regardless of the 5kg single block locations you can then move the position of the mystery object until you find a configuration that balances the system.)

Answer 1

No, it is not possible.

From the statement here and from what I understand, there must be one known mass on one side of pivot and one "mystery " object on other side, so we need to move the mystery object or the known mass in such a way that the beam is balances ( means it is perfectly horizontal)

you need to know one mass at least, with both masses unknown, you cannot use equilibrium condition involving torque.

To find the mass of mystery object, you can just find the torque of known mass and divide it by lever arm of mystery object.