Move an object from A to B to C etc.?

I understand that you are controlling the moving through a platform and A, B and C are checkpoints in your way.

You must clarify this, if you want the movement be automatic, if you want to move it with the click of your mouse, or if you want to use the key arrows.

For falling, you just have to add a Rigidbody component to the game object your are moving. When the object leaves the ground, it just falls to the abyss. To attach the Rigidbody, select the game object, then go to the Component Menu, then Physics, then Rigidbody. Once you have attached the component, check if "Use Gravity" is checked.

I hope this helps, but answer and we'll try to solve the other questions. :D