Oops, my post above regarded beam weapons. Missiles are not affected by atmosphere.
Just to make this clear (I have also edited my post).
As for starbases:
They are just ships without engines and will stay in orbit over the planet they are build.
The only way to move them is with tugs (ships with a tractor beam). You select the target they should pull from a drop-down on the individual ship screen (F6, I think), miscelaneous tab.
PDCs are _not_ movable, after being build (they are supposed to be deep underground (think cheyenne mountain) but can be pre-constructed in parts. Those parts can be transported to the planet/moon/asteroid you want them to be and assembled there (some factory capacity, either actual factories or engineer brigades, _and_ some minerals are needed for this). After assembling them, they can not be moved again, just like a regular PDC