We can see things moving faster than light

Hey Physics Girl, can you tell me, please,  - are space and time or spacetime a physical substance or those are a mathematical construct? On one hand neither space nor time have any physical properties that would make them some material substance, on another hand physicists constantly talking about space and time as if they are something material that actually can warp, expand or dilate. So what is it ? 
The second thing is  - how sure are you about galaxies or groups of galaxies moving faster than speed of light? I understand, you’re talking about spacetime expanding, but the thing is that you’re talking about very, very specific places in spacetime. Because, as far as I know, the neighboring galaxies or groups of galaxies don’t have the same redshift caused by Doppler effect. And it means that either space expanding only in very localized areas or that, what is most likely, redshift isn’t caused by Doppler effect, but by some intrinsic properties of those specific galaxies. So, Physics Girl, which is it? Is fabric of spacetime a real, material substance without any physical properties whatsoever? Or is it just a mathematical construct, like many others things we use: length, width, height, distance and so forth?