Tricky math questions!

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Hm, I don't know if there is a smart way to fake 3D movement with a point. You can try to move the coordinates of the 3D point by user input. I.e.
Key Up - decreases z
Key Down - increases z
MouseMoveX - de/increases x
MouseMoveY - de/increases y

Then I would try to fake depth by making the point bigger the nearer you are to the point which means the nearer the z value is to zero the bigger the point. If z is negative the point is behind the camera (this is fake because a point is always the same size nevertheless how far away you are from that point).

If you want to make it correct (like a real 3D engine does), you will have to use vector and matrices math.