This is a tough one, especially as I'm not used to giving explanations in non technical terms.
Starting at the top:
Conditionally yes. In the emptiest space possible - not that between stars, not that between galaxies, not that between families of galaxies and so on..... in the very emptiest space between the super-clusters of galaxies, there it's at its fastest, where gravity is at its weakest.
If you had the time to do so, and a nice clear target black hole and shot a blue laser just at the event horizon on one side (say it's transmitting the whole of the works of Shakespeare followed by the rest of project Gutenberg) - in such a way that it skimmed all the way round and then exited back in your direction, like a slingshot of the moon the first orbit of the moon did, what would happen? Would the light colour change?
The closer the beam got to the event horizon the more stretched space is - think of it that way, then the light has to travel further, and the same all the way round the black hole - the closer to the event horizon the deeper the well, the more the space is stretched and the longer the light takes to get around. From your point of view, the black hole is X distance away, the path the light took is Y in apparent length. Using your handy slide rule you calculate the Taming of the shrew should arrive at time Z.
It doesn't turn up on time. Why? Remember the light had to take a very long path because of the gravity field density making the journey longer. When it does turn up finally What colour is it? Still blue - this does not depend on if the black hole is moving away or closer - there is no red or blue shift.
(I am being slightly disingenuous here as the wavelength would have shifted a minute amount to the red - it does this as it travels, the further it does the more it shifts, partly from collisions with free floating atoms that absorb then re emit at a lower frequency eg. the big bang (Very hot) - the light from this is very long wavelength indeed, (red shifted to the extreme) but space is expanding remember. To put it in a nutshell, entropy cannot be reversed.
The odd thing is the distance the light travels from the point of view of the observer who shot the laser, he would extrapolate that the light waves containing The Shrew, since they arrived so late must have not only slowed down but gotten closer together (blue shifted) - but when it comes back to the observer it's just the same colour as before. (Space lengthened apparently, that would explain this wouldn't it?)
To say that gravity slows light is the same as saying a watched kettle never boils, it has a kind of truth to it from a particular point of view - a perceptual point of view.
Looking at the whole universe, there are visible hot spots and cold spots, places with more and less matter - this can be observed. The trouble we're having at the moment is with dark matter, and dark energy.
We started with observations in our own solar system. Distant objects are all measured relative to each other. A large number of observations are made of many objects, their luminosity, their aggregate luminosity, their red or blue shift - and interestingly their change in Doppler shift. Various different type of star, pulsating ones, stars that emit hard radiation, co-orbiting stars of all sorts, the accretion disks at the center of galaxies and their temperatures, This accumulation of data since Copernicus, or at least since the Renaissance has all been put together, adjusting along the way taking into account world changing paradigm shifts such as relativity, and huge advances in the resolution of our observations of the universe, from land and space based platforms has (we think!) made our estimations of the error margin of our calculations of the age of the universe smaller and smaller.