Why is the moon that special? Is it really a well built coincidence? I find it funny that the moon is the only object in the solar system to almost perfectly fit the sun, resulting in the spectacular solar eclipses. No other object except maybe a few irregular moons like Pandora from Saturn would do that, and for them, they aren't round, and thus can't fully block out all light. The moon also has a perfect rotation that is almost exactly the same as Earth's rotational period, resulting in a tidal lock, which causes tides. 

Is this a coincidence? Any speculation on why this happens? Is this the only observed place where such criteria play into such perfect coincidence?
If the "perfect rotation" you describe is the fact that same face of the moon always faces the earth, this is explained by the 'Giant Impact Hypothesis' which also explains the formation of the moon. The molten earth was impacted by a large mass causing a part of the liquid earth to be flung out into space creating the moon. For a time, the two celestial bodies to be (the earth and moon) were connected to one another by some bridge of mass until eventually the centripetal force of their rotation finally pulled them apart. In fact, the two bodies are still moving apart today. 

https://en.wikipedia.org/wiki/Giant-impact_hypothesis