It does, but only vaguely unless you already know how it works and can work backwards to Newton's laws. Eg Newtonian mechanics can explain how flying works, but if you don't already know then it's hard to go from Newton's 3 laws to a functional explanation of why planes don't fall out of the sky.

Some of that is also the domain. It's less that science is an extreme form of compression, and more that natural phenomenon are highly compressible. They're a small number of kinds of interactions repeated a bajillion times. How many equations does it take to explain electricity (ignoring equations that are derivatives of ones already included)? I think it's less than 5.

On some level, you could probably reduce all of the Standard Model down to models of atoms, their motion, and the basic subatomic particles (the non-quantum ones). That would explain almost everything that happens on Earth in a very short form, though few people would be able to go from that to explaining how lightning works.

Yes. But /lossful/ compression: (scientific, philosophical etc.) laws compress an abstract narration of events into that tiny, hard, fundamental, predictive detail.

(Then it depends on your concern: "Aagh, the aunt fell!" // "Oh yes, that'd be Newton")