Reality is made out of language and meaning, although the scientific models still describe things (phenomena) pretty well. We have the concept of vacuum, which is similar to the Eastern concept of void (non-scientific term, more spiritual or philosophical than anything else). It can be quantified in either energy density or gravitational potential. Exotic matter (dark or non-baryonic matter) could complicate it more these days, since when I was a kid over twenty years ago we didn't really know what it is. You would still be able to measure a vacuum, though.
Measuring the amount of space in the sky is really only important to specialists in the field of cosmology. You could very well take the masses of galaxies and approximate the empty space in between, including subatomic and virtual particles such as neutrinos and gravitons or anti-matter, and anything giving off friction as energy adds to the total of all that.
We know some of the shape of space because of the cosmic microwave background radiation, which is a notion that supports the Big Bang. The variation in spatial density indicates non homogeneity, or the result of the cooling of extremely hot, plasma temperatures, based on the initial settings of the universe.
Leibniz had a more philosophical approach to space whereas Newton solidified the science aspect of it. We know that Newton laid the foundations of absolute space down in the late 17th century before Einstein updated it, saying it is relative, in 1905-1915. Leibniz said it was spatially relational, which sounds relative, and this is the aspect people talk about when they say Einstein plagiarized relativity.
Absolute or relative space could mean everything is one. According to Leibniz, if space consists of relational points between objects, God would have had to think where to put the universe, as opposed to any other location. How important would that be? The opposite would be that it wouldn't so much matter, if there was no direction in space, any other place the universe in would basically be the same. We wouldn't be able to shift to a different universe.
It's illustrated in the bucket of water example, wherein if you spin it it accelerates, and the water doesn't spin until a certain velocity is reached. Space is the water and universe the bucket. Leibniz said you could move the whole bucket. Newton said the water only moves if the bucket does, and that the bucket doesn't necessarily exist.
Newton's 1st Law of Motion: Inertia - an object in motion tends to stay in motion, and one at rest tends to remain at rest, as they were, unless acted on by forces, such as friction.
2nd Law - F=ma
3rd Law - Every action has an equal and opposite reaction. In order to move a boulder, one must apply more energy to it than its mass contains.
Air is really another layer, above the ocean - it's an ocean of air that we breathe, oxygen and carbon/CO2, because we can't breathe water anymore (no gills). Space is a lack of it. We are, in a sense, still connected through that. Space could be more equilibrium in an environment. A core, planetary or stellar, is a huge mass exerting gravitational influence. It warps spacetime causing it to sink. In one sense, it's what's on the other side if any two points in space could be connected. It wouldn't be the most efficient way of transferring information, so to speak.