The laws of motion as you refer to them, are a part of Physics, so no mixing needed
They may be first encountered at gsce and A level in the form of sugat equations, and also parts of A level  pure and applied mathematics in more detail


I am not sure who ‘they’ are, but if I assume it’s either Physicists or Scientists in general then it sounds conspiratorial in nature, when I don’t think for a moment it is. There are some misconceptions about theory and ‘laws’ especially in popular media. Some of those have been tested and validated  over many years and as such it would seem foolish to reject them on some whim, because we may be missing a part of a bigger picture. If that was the general view, we would have progressed very little. Given what was known about chemistry and atomic structure, it seemed perfectly sensible to support the periodic table, even when there were gaps left for elements we had not yet discovered. I dont see that it matters much what they were called

The gravitational force exerted in relation to two bodies is inversely proportional to the distance between those two bodies, ref para 1) but that would not accelerate them in terms of moving apart as it has the wrong vector direction, unless they were subject to another force

I don’t see that it matters in itself what term is used to define that

As for precision, there is some which is unavoidable, in fact I would say essential, other caveats eg like needing an inertial frame of reference are usually left out at certain levels

If some see Scientists as just sitting there, whimsically thinking up some notion or other, I would say thats very much mistaken