The first of these vintage greenkeeping tools, which has a fork-like appearance, is an aerator that is operated by pushing the forks/tines into the green.  Because the tines are all hollow, the punched-out grass plugs will come out of the top of each tine and collect in the box atop the tines.

To operate the second tool, which has a small handle, the greenskeeper would push down on the top of the tool. This would drive the four spring loaded prongs into the green and repair ball marks.

The third tool has two handles and two pronged "feet" at its base.  After sticking the sharp prongs of these feet into the green on each side of a ball mark, the greenskeeper would squeeze the 2 handles together, and that would move the feet closer to each other, thereby repairing the ball mark on the green.