Is it possible for a planet to have a perpetual solar eclipse if a satellite orbits at the same speed as the planets rotation?
Kind of, but it's not very stable.
In this arrangement, the satellite is at the "L1 Lagrange point". This is where the gravity from the planet, the gravity from the star, and the effective centrifugal force from movement of the planet and the moon all cancel out, and the moon is at an equilibrium point in-between the planet and the star.
However, this is not a stable equilibrium. Although all the forces add up to zero (in a rotating frame), if you give the moon a tiny push, then it will drift away further and further and faster and faster until it's not near the L1 point anymore.
This means that you don't get moons naturally hanging out at the L1 point. But you can put an artificial satellite there. You do need to constantly give little boosts to correct the orbit to keep it there, but they only need to be small boosts.
Quakes are generally accompanied by very sight rearrangement of a body's mass which is accompanied by a movement of the center of mass.
For a thought experiment, imagine one half of a planet were hollow, but then the whole thing collapsed uniformly in space. The new center of mass would be moved significantly towards the former empty space, resulting in the gravitational effects being different. Real quakes do the same thing, just many orders of magnitude smaller.
Do Earth earthquakes, or crustquakes of other bodies, perturb the Solar System's dynamics at all?
Technically, yes. Practically, no. Our Solar System is very spread out and Earth is nowhere near the biggest player among the planets; pretty much no earthquake it could possibly experience would have any kind of practical impact on the orbit of any body (even the Moon would barely be disturbed).
To put this in context, if you performed the "doomsday scenario" of a "planetary alignment"—that is, line up every single body in the Solar System perfectly—so that their gravitational fields were all as impactful upon one another as possible, NASA calculated that it would be enough to cause Earth's tides to rise... 1/25th of 1mm.
What earthquakes certainly can do is affect the rotational speed, tides and axial tilt of a planet, because it's a redistribution of mass within one system over a relatively small area. However, even there, the effects are generally very minor. Remember the 2004 Christmas Day tsunami and earthquake that killed over 200,000 people in Indonesia? That earthquake did actually cause the Earth's rotation to speed up somewhat, and shortened a day by about 3 microseconds (3 millionths of a second) because the Earth got a bit less oval-shaped. However, since the Moon is consistently stabilizing our orbit, that change in rotational speed was lost likely within a couple of weeks.
we named the planet "dirt". an earthquake is a quake of earth not a quake of the earth so an earthquake on mars would still be an earthquake.
(edit- ...i guess it wouldn't translate to for example planets "made of ice" instead of a quake of some kid of rocky crust (like if a miles deep glacier shifted), if you're being overly literal with the roots at least. common use would probably still call it earthquake as long as 'the ground' is shaking regardless of what the ground is made of, like how acid rain on venus is still rain. but it might matter scientifically since I'm not sure if ice layers can really be described as having plate tectonics /edit)
changing it by planet would be silly, like how fireman is linguistically correct even if ignorant people who don't know what the word actually means decided it wasn't pc. I'm sure somebody would insist on calling it a marsquake but they'd be wrong
"Earth" translates if you think of the meaning as being "our earth, our planet." If there were Venusians or Martians and they had a word for their own planet it would mean the same thing, it would be the translation of "earth" in their local language. "Earth" is a relative term.
Isolated cultures don't themselves give a proper-noun to their own island or their own people; the word they use in the local language just means "the land" or "the people." Because for them it's the only land, the only people. Or you'll find the name was given by outsiders and eventually adopted by the locals, because we do give proper names to other places, to other people.
So "earth" should be written with a lower-case e because it's not a proper noun.
What about on the other side? Is it more stable if a planet is in the L1 point between a smaller moon and its parent star? So if we lived on a planets moon could a planet permanently eclipse the moon and be relatively stable or because the planet has greater mass would it be even less stable than a smaller object in the L1 point?
Also side question how many Legrange points are there where Gravities cancel each other out? Are they just in smaller star-planet-moon systems or do Galaxies and star clusters have legrange points?
When the moon is "behind" the planet, it's in the L2 point. The Lagrange points are defined relative to the planet because it has a stronger gravity. But it's also unstable.
There are five Lagrange points in total. Wikipedia has a nice plot but I'll list them here:
L1 - satellite is between planet and star
L2 - planet is between satellite and star
L3 - satellite is on opposite side of star from planet
L4 - satellite is partially anticlockwise around the orbit from the planet
L5 - satellite is partially clockwise around the orbit from the planet
Out of these, only L4 and L5 are stable, and they only exist if the planet is sufficiently small compared to the star. This is the case for all the planets in our solar system - even Jupiter - but it means that two stars orbiting each other do not have L4 and L5 points.
However, for Jupiter they are quite deep and stable, and they are home to two "camps" of asteroids: the Trojan asteroids and the Greek asteroids, who hang out in the same orbit as Jupiter, one "camp" in front, and one "camp" behind. Again, wikipedia has a nice plot.