Can I move plot-specific buildings ?

Yes, you can. You will only lose money and building time.

In particular, destroying and rebuilding alien containment is a way to kill all aliens in it, so you'd have their corpses for the Grey Market or Council Requests. This is the only way to kill of duplicate aliens, as you can interrogate particular kind of alien only once. Duplicate aliens just sit in the Alien Containment forever, providing no added value whatsoever.

You can with some of them, but not others. The Gollop Chamber and the Hyperwave Relay cannot be demolished once you've built them, so try to build them where they will not mess up your base's layout. You'll spend time, money and materials rebuilding demolished facilities, as well their use - demolishing an officer school will deactive all the upgrades you've bought there until you build a new one, for example.