Have the Sun an influence on Moons speed in its orbit around the Earth?
The sun acts more on the earth-moon (earth and moon) as a system. The moon, and the earth, both act on each other. Over the long run (billions of years), the earth predominates and the moon will break up into a ring (unless humankind intervenes). The speed of the whole earth-moon system in orbit about the sun varies, being somewhat faster at the closest-to-sun points of the ellipse. Detectable by astronomers. So, right there is a Yes for moon’s orbit around the sun. As to orbit about the earth, the influence of earth exceeds the influence of the sun, however, the sun does both slow and speed up the moon slightly, as it departs and as it approaches to sun. Yes, to your main question, about orbit around earth. The changes sort out into long cycles mentioned in other answers here. Since the changes are small, the cycles are long. I would think tensions are greatest when moon perigee* and solar eclipse coincide. Never heard about eclipse earthquakes yet, will have to google that.******* *o
