Are handstand blocks useful for improving the handstand?
Yes. As an added bonus, most people find balancing on blocks to place less stress on your wrists. You can even get/build blocks that slope to reduce wrist stress even more or if your wrists are not very flexible.
Typically when balancing on the floor we have more weight near the palms, and leave the fingers relaxed until we need them. This results in overuse of fingers balancing and less shoulder balancing. On blocks you wrap your fingers around the blocks. Tensing and untensing your fingers around the block doesn't do much so it will force you to put more weight near your fingers and balance more with your shoulders.
Are handstand blocks a good start for learning the one arm handstand?
Absolutely. When in a one arm handstand you want to be balancing with your shoulders primarily and blocks help to learn that. Once you are close to the one arm handstand, you can transition nicely onto canes since they have blocks on top of them. The slight wobble in canes actually make handstands and one arm handstands easier once you get over the nerves that come with being higher up.
What exercises can be done on it?
It depends on how tall your blocks are, or if you are stacking blocks. The more ground clearance you have, the more you can do on them. There really isn't anything you can't do on them that you wouldn't normally be able to do on parallettes of equal height. Some examples are L/V-sits, Planches, Handstand Walks, etc.