IIRC, you do get some nominal amount back. In my current game, I just flipped a planet and decommissioned the influence bases I had built around it and got 40 BCs fo9r each. One had no extra modules and one had a 25% bonus module on it.
I do not know if one gets money back for destroying mining bases or asteroid field mining facilities. It would be simple to test, but I won't be able to game until late today at the earliest.
One point to consider is that, after the first few non-mining bases, each successive base costs more and more. Thus, even if you get ~0 back, destroying no longer needed bases reduces the cost of the next one you build.
Oh - and yes, they cannot be moved.