What are the chances of a moon orbiting a planet with the same orbital and rotational frequency?
I have never heard of an explanation for the Moon orbital and rotational time being the same.
Only one thing I can think of. The gambling dice. Thw way to cheat is to have the gravitaional certre of the dice moved from the geometrical centre.
If the centre of the Moon is offset - one side is havier than the other - the havier side would always turne towards the gravitational force of earth.
Not even earth have his gravitacional center really in his center! For that to happen, earth, moon and all the planets would have to be perfect spheres, which is not the case. We consider, however, that it is in the center, once the mass of all the planets, including Moon, are extremely high and does not affect anything about that you said, i mean, it affect, but it is so despicable when compared with the masses that we assume that does not affect!
About the same period time of the earth and moon. I not sure, but the chances i think that are very low! Also, it is possible to happen because there are some circunstances that make it possible to happen. Those circunstances are the masses both from moon and earth, which causes the correct distance between them.
Finally, the Sun also provoque changes of the orbit from moon and earth! The Sun’s gravity sometimes causes the Moon to speed up or slow down slightly in its orbit. This compensate everythime the moon is at a diferent distance from earth (having in mind that orbits are ellipses)!
I´m not telling all the factors that work here for that phenomena happen, but i think you got the picture!