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I have no idea if/how the two concepts are linked, that of everything being in motion and there being no absolute motion. I believe both are claimed by contemporary physics, and e.g. Descartes, and there is a lot to read about the relativity of motion in e.g. Galileo, Newton.
If everything is in motion, then is all motion relative?
All motion is relative, to the limits of our capacity to measure it. This is a bedrock principle in physics due to Einstein which replaced the Newtonian/Galilean idea of absolute motion as a more correct description of the universe we inhabit.
All objects (atoms, etc.) above absolute zero temperature are in motion.
Inertial motion is essentially relative. The idea of absolute inertial motion is effectively meaningless-all it can convey is that a particular frame has been picked to be the baseline for quantifying motion, and any inertial frame can serve that purpose so the selection is necessarily arbitrary in an important sense.
You might get another perspective on the principles concerned if you imagine that everything in the Universe could suddenly be frozen so that nothing whatsoever moved. You might consider that to be a state of absolute immobility. But then imagine a variation on that set-up, in which everything in the frozen Universe was moving en masse in a common direction at ten metres per second. How could you compare the two scenarios? How would you know which of the two was stationary and which was moving? The answer is that you couldn't- indeed the distinction between the two scenarios is meaningless, because if you say something is absolutely stationary, or moving at such and such a speed, in both cases the obvious question that arises is 'relative to what?'.
It is most useful to conceive of motion as a rate-of-change of position, so it presumes an established system of position. The philosophical question that then arises is whether there can be any absolute system of position that does not depend on the position of particular objects (or sets of objects) or whether a system of position must be only relative with respect to one or more existent objects. To put it another way, is it philosophically coherent to for the whole universe in toto to move?
Descartes took the view that the position of objects must be considered relative to other objects, and therefore motion was always relative to the position of other objects. He considered that when people would make statements of motion without explicit relational objects, this implicitly referred to motion relative to some contextual surrounding. In this sense, he believed that there was some natural or "true motion" relative to some natural/obvious surrounding context (though this is largely an epistemological issue rather than a metaphysical one in my view).
One way to assert an idea of "absolute motion" is to pick one or more arbitrary "fixed points" in space and measure position and direction relative to these (e.g., one could take four fixed points to establish a three-dimensional coordinate system). The difficulty of this approach is that it relies on alleged "fixed points" that are not themselves moveable objects in space (for if they were objects that could move themselves then you would be back to a relative position system). The difficulty with this approach is that such points are inherently unobservable, so the "absolute motion" of objects then becomes unobservable. Leibniz famously critiqued this "absolute motion" approach, saying that since absolute velocity would be unobservable, it is really just made-up.
Of course, you are right.
I believe your main questions are not about the three philosophers. I believe they are, 1.'Would the existence of an absolute mean not everything is in motion?', 2.'If everything is in motion, then is all motion relative?' In other words, you have a doubt 'absolute existence' and 'relativity' also. So I shall try to answer connecting all these, without mentioning Descartes, Galileo or Newton. The knowledge about the 'thing' that relativity does not operate, is ancient. To get an answer to your question, you need not even seek the help of these three.
Among ancient philosophies Advaita philosophy stands close to your idea. To represent that absolute mean we use the term, Brahman. If God has other duties even God can't be treated as the absolute mean. So, more precisely it is treated above God. The answer to your two questions is 'Yes'.
https://en.wikipedia.org/wiki/Brahman
Gita says: https://www.holy-bhagavad-gita.org/chapter/2/verse/25
