In any case it would be an obvious stepping stone to places that were of economic benefit. A forward base. Plenty of colonies weren't particularly important themselves but ended up being crucial because they allowed access to ones that were.
Yes. We're lucky we even have the Moon, dead as it is. If we had no such natural stepping stone, I doubt we'd even have any space programme at all (assuming humanity developed as in OTL of course).
Having a re-fuelling station using the hydrogen/oxygen mined on the Moon would decrease the cost of interplanetary missions by a factor of ten (approximately), since propellant inevitably makes most of the mass of any interplanetary mission. Of course, when we're there, we'll likely find other uses for the lunar station - we could perhaps build the low-tech parts of space vehicles there (aluminium pressure hulls, solar panels, etc.) as well and thus save us money having to launch them from Earth, which is many times more energy-expensive than launching them from the Moon and assembling them together in, say, the Lagrange points.
Really, it irks me when people say nonsense like "
the Moon is useless, there's no point in going there at all". It's based on utter ignorance of all the possibilities Luna offers to anyone who is bold, or forward-thinking enough, to take advantage of them.
And then there is Mars, of course, a world that could be made into a second home to humanity in a span of just a few centuries - probably in the same amount of time it took to turn a few colonies in the Americas into what they're now. As you said, all that could have been Chinese. Instead, it's western. Sometimes I wonder if the Chinese-speaking native Martians in 2500 will be equally amused when thinking about the mistakes the West did in early 2000s
I think radio telescopes are much easier to build but need to be very large, so making a free floating radio telescope is hard.
I don't know if installing a telescope on the moon is easier than one in space. Besides, free floating telescopes can aim in every direction, while a moon telescope is limited by its position on the surface of the moon.
Free floating telescopes needed for exoplanet imaging will have to fly in very precise formations (we're talking nanometres precise) and be permanently shielded from the Sun to remain cool enough to be able to function. Turning them "in any direction" will be hard to say at least.
Having a stable rock underneath and the natural shade of crater walls (for most of the year) as well as astronauts nearby ready to replace damaged mirrors or burnt out motherboards would be of great advantage. True, such telescopes wouldn't be able to look at the whole of the sky, but that's not necessary. A set of identical telescopes on both Lunar poles would be able to look almost anywhere - not always, but since observations generally take a long time, it wouldn't matter.
So tell me when they announce or do that. Your thoughts on the subject do not translate to Chinese policy, no matter how much you'd like it to be so.
Which is why I include words like "if"

China's behaviour in space so far leads to this conclusion.