Is construction serial or parallel? (In other words, can multiple building/excavations happen at once, or is it one at a time?) If it is serial, is there a way to control which happens first? Does number of engineers matter beyond the building requirements?
You can construct any facility at any time. The only requirements are having the money and engineers required to build it and also that the tile is accessible: excavated on a level with lift access.
Excavation can also be done while you construct or excavate another tile of your base, as long a you got the money.
Here's a image to show you it is possible:
You can build as many facilities and/or excavations under construction at the same time as you want, assuming you can afford them all of course. They will all be built at the same time and won't be any slower.