Is it a coincidence that the size of the Moon and it's distance from Earth compared to the size of the Sun and the Sun's distance to Earth....
There's no coincidence, the moon is the end result of a nearly Mars-size planet striking the Earth back when our planet was still molten material in a big accretion disc around the sun. The Earth and our moon are made of the same stuff, but the moon lacks the big massive iron core that ensures enough gravity to hang onto any atmosphere. Basically, the moon is chemically the same as the Earth, except that it's been sterilized over a couple of billion of years by the Sun's radiation.
Is it a coincidence that we have perfect eclipses?
No, considering that most of the planets are on basically the same plane around the sun. The fact that they occasionally line up just comes with having multiple planetary bodies moving on the same plane at different distances and speeds.
Basically when we look up in the sky the moon and the sun are basically the same size.
Only now... but when the moon first formed, it took up most of the sky because it was so much closer. As our moon revolves around the Earth, it also travels farther away... currently at a rate of almost 4 centimeters a year. One day it will eventually be so far out that it drifts away into space, but by that time the Sun may already be a red giant so it won't matter, as we'll all be charcoal.
Considering that there are hundreds of stars that we know about (and probably billions that we don't) with planetary satellites, it either means that physics dictate that objects of a certain mass, chemical makeup, temperature, and a few other factors wind up creating planetary systems that are predictable (a star of a certain mass, stable for a billion years or more, with an accretion disc, typically creates some sort of system when heavier elements are attracted, forming planetary cores, then followed up by the accumulation of matter with less density, creating atmospheres, ice, gases etc).
Either that or the creator is obsessive compulsive and when he's not making galaxies, he walks around parking lots memorizing license plate numbers for no good reason.