Do pirate yards even exist? Shipyards are kind of a big affair and would certainly require some extensive mining operations to support. Seems unlikely that the IoM wouldn't spot something like that and wouldn't get rid of it.
Yes they do. Generally hidden in asteroid fields, or out of the way systems, sometimes in even more out of the way places like warp storms.
The IoM has nowhere near enough resources or territorial control to find and destroy all pirate bases. Although doing so is definitely part of the duties of the Imperial Navy.