(This is the third in a series of questions, starting with Moved into further orbits to protect them, how much damage do Earth and Moon take when the Sun expands? and How soon does the Earth's surface re-solidify after the red-giant Sun is replaced with a different star?)
The story so far:
To recap from my previous questions (and @StarfishPrime's answer to the first): Far future humans have attempted to save the Earth from destruction at the hands of an expanding Sun, by moving it and the Moon into a further orbit. They didn't, however, get them to a sufficient radius to save them completely. Giving up, they abandoned the solar system.
A group of aliens, wanting to preserve something of the Earth and Moon for scientists to land on and study, arrive shortly after this and take action. They have brought a large gas giant (at least the size of Jupiter) with a solid rocky/metallic core, and by steering it into a very close orbit, ensure that it is engulfed by the Sun when it starts to expand. This eventually causes the Sun's red giant stage to end prematurely, as it sheds its hydrogen envelope. Thus, it becomes a type B blue-white subdwarf, similar to Kepler-70.
Nevertheless, the Earth and Moon have taken a lot of damage. Tens of millions of years later, another group of aliens arrive to witness the results.
The heat and escaping gases have burned/evaporated away the Moon's crust and most of its mantle, reducing its diameter from $\approx 3500 km$ to $\approx 700 km$. The Earth has fared better, its diameter being reduced by $\leq 130 km$. Depending on how soon the second group of aliens arrive, the Sun may still be the blue-white subdwarf, or may have become a bluer Type O subdwarf, or may even have gone past that stage to become a white dwarf.
And now... the question!
What do the Earth and Moon look like now? In particular, what colours do their surfaces appear to have, and has the Moon developed new "seas" on the side closer to Earth?
What my research suggests:
Let's start with a diagram of the Moon's geological layers - I think it will help clarify the reasoning that follows:
In the case of the Moon, if the stratified layers of its geology were not mixed up and rendered homogenous by the increased heat, the less dense materials in its crust and most of its mantle would have been lost. The heavier materials of the iron-rich core would have sunk back to the centre, leaving exposed the pyroxene and olivine of the lowest mantle region (the "zone of partial melt".) As this resolidifies, it may resemble the darker basalt of the Moon's seas/maria. However, coming from lower regions of the mantle, it might also be mixed with some iron (silvery - dark grey) and a little sulphur and/or iron sulphide. It could also be that the pyroxene and olivine are less mixed, resoldifying as green crystalline areas.
If, by contrast, it was rendered relatively homogenous as the layers mixed, we might still expect the lighter elements (currently nearer the surface) to evaporate first. The Moon's outer layers are relatively light in colour, so I think the new, smaller Moon might look a little darker.
That's before one considers the different wavelength of the starlight now reflecting from it, though.
I understand that the reason for the maria being only on the near-side of the Moon is not currently known, or at least that there's no consensus on any one theory.
In the case of the Earth, I think I'll need to plead even more ignorance. The atmosphere might resemble that which it had before photosynthetic life began to increase oxygen levels (CO_2, nitrogen, some other gases) or might be maybe hydrogen, including the layers shed by the Sun. The resolidified new crust underneath this might look somewhat similar to the present-day crust, possibly varying a lot from place to place. Without there being another Large Heavy Bombardment, I don't think there would have been much new water introduced to the planet, and with the loss of oxygen there would be less for the hydrogen to react with. So I think there would no longer be any large oceans, and plant life would not have re-evolved in any form in so short a time either.
Perhaps it would resemble present-day Venus? But with more hydrogen, due to the magnetic field continuing to function. And without sulphuric acid in the atmosphere, it wouldn't have the yellowish sky and opaque atmosphere of Venus.
(Disclaimer. As you have all probably guessed by now, I'm not a geologist! Or a chemist, for that matter. So you should take my reasoning with a pinch of salt.)
Weber, R. C., Lin, P. Y., Garnero, E. J., Williams, Q., & Lognonne, P. (2011). Seismic detection of the lunar core. science, 331(6015), 309-312
Heber, U. (2009). Hot subdwarf stars. Annual review of Astronomy and Astrophysics, 47, 211-251. Plus slides.
Wieczorek, M. A., Jolliff, B. L., Khan, A., Pritchard, M. E., Weiss, B. P., Williams, J. G., ... & McCallum, I. S. (2006). The constitution and structure of the lunar interior. Reviews in Mineralogy and Geochemistry, 60(1), 221-364.
And quite a few Wikipedia pages.