The Region Manipulator does not provide any ability to move stuff onto the current world tile. It's completely focused on manipulating things within it.
Blocks of 3*3 world tiles, to get 9 different biomes. This is simply a descriptive term for this particular purpose and doesn't have any relation to any in-game structures (apart from the world tiles themselves, of course).
If you move a town/fortress/forest retreat (and their variations) the game still thinks it is in the original location for some purposes. My experiments (now a few years back) of trying to move the starting site of civs caused new settlements to be set up around the original location, or fail to generate any new settlements at all if moved to a different land mass. There are obviously ties to something I don't know of, and that might not be mapped by DFHack. Necro towers have been moved without any visible issues, although I don't know to what extent they've been tested to verify that they'll actually attack a fortress they've been moved next to.
At the time the Embark Assistant was written the DFHack structure info describing lairs was a lot more unclear than the current one, so the implementation only specifies that there's a lair at the location, but not the type of lair. If I remember correctly from the restructuring of the DFHack info there were two lair sub types described as night creature ones, but it seemed one of them could contain just about any kind of creature (including night ones), while the other seemed to be exclusive to night creatures.
Regardless, I'd use Legends Viewer to check that there's actually a desirable creature in the lair before embark, as I assume you don't want an empty one.
If you want to search for lairs I'd suggest writing a script to search the site vector for the types you want to take a closer look at.