Do I have any authority over airspace above my land?
In the US you have, effectively, zero rights over the airspace above your land by default: Control of airspace is entirely delegated to the FAA, and they're super serious about it.

If you designate your land as an airport you can certainly establish a control tower and request an airspace designation from the FAA - whether or not they approve your plan depends on the existing airspace around you though: If your airport would create a problem for an existing airport you'd probably not be able to get an airspace designation for it, and it may even be classified as an objectionable airport.