How long after fuel stops flowing before the engine quits?

Yeah....do not do that...

  I know at ide often a student forgets to turn on the taps and they seem to get about a minute at 2-3000 so say quarter that at power setting, maybe only 15 seconds ?

This will not hurt the carbs by drying them out or the engine. Athough the impact with the ground will not be good for the engine.

I checked this as a part of my initial 80hp 912 UL install at 1,800 idle rpm speed.  It took nearly two minutes (warm engine) after I shut off the fuel valve before the engine started to stumble. That made me vow to never hurry my ground checks and take my time before launching. 

It ALL depends on your fuel system and every aircraft is different! Some may last 2 min full throttle and some will only last 30 seconds. 

When my checklist says to check the left and right tanks do I wait for a few minutes then? What would be the purpose of verifying left and right on the fuel selector if you're only switching it over for a few seconds? None probably so I should leave it like that for a few minutes before switching back during run up?

I find it somewhat disturbing that some airframe manufacturers have the pilot "switch fuel tanks" or "test fuel tank selector" as part of the pre-takeoff / run-up checklist.  If you switch to an empty tank or a problematic fuel feed you might discover the unfortunate consequences right after lift-off or on initial climb-out. If you desire to check the fuel tank selector I suggest that you do so early in the engine start-up process thus giving sufficient time for a problematic fuel feed to make itself known while safely on the ground.