Within the US: When, and by whom, is the Transition Level determined/published?
The "Lowest Usable Flight Level" ("Transition Level" [TL] - term used outside North America) is FL180 when the (local) altimeter setting within a controller's area of jurisdiction is 29.92 inHG or greater. This is normally, not necessarily always, the province of ARTCC controllers in the U.S.

Your Questions:


  Is the entire US using the same TL at any given point in time?



This is not the case because the local pressure in San Francisco can be (for example) 28.92 and the pressure in Miami could be 30.20.  Therefore, the lowest assignable/usable FL over San Francisco would be FL 190 and the lowest assignable/usable FL over Miami would be FL 180.


From FAA JO 7110.65W, para. 4-5-4: JO 7110.65W




  Or, are individual ARTCCs setting their own TL based on the lowest QNH reading in their geographical area?



Individual areas of jurisdiction within ATC Facilities would be responsible for determining the Lowest Usable Flight Levels based on local QNH/altimeter settings.  Keep in mind that some sectors (areas of jurisdiction a single controller may be responsible for) can be enormous in size (part of Nevada west to near San Francisco, for example).  There can be a significant difference in local QNH settings within that sector that may require adjustments to the Lowest Usable Flight Level. 



  Or, are individual sectors within an ARTCC setting their own TL based on the lowest QNH reading in their even-smaller geographical area?



See the answer above.
and 5. In my experience, an individual controller maintains all separation authority and responsibility within his/her assigned sector.  There may be supervisory input or oversight, but the responsibility to separate aircraft in accordance with the JO 7110.65 rests with the assigned controller.  There also may be internal SOP's that dictate how a facility will handle the flow of the information regarding lower than 29.92 local altimeter settings.