I feel like this video
https://www.youtube.com/watch?v=HkPFZWd8wj4 does a nice job of explaining how meth works.
Generally speaking, meth is sprayed based on boost pressure, so once the boost reaches a certain level, the spray kicks in. As far as how long it lasts, I don't have the ability to give even a general range (X miles or X gallons or whatever) because I don't have it on mine, but you can logically conclude that the heavier your foot, the faster you'll go through it.
As far as driving on an empty meth tank, that would be a question better answered by someone who has a system currently. From what information I do have, I believe the answer is "sure" but you'd want to be very careful to stay below the meth injection threshold because I believe that's when you'd start to see the advanced timing that takes advantage of the meth injection. If you're getting advanced timing but not getting meth to the cylinders, you're asking for a heap of trouble. The good news is I believe the methanol mix recommended for the kit Torrie sells is pretty readily available.
My single biggest concern with meth right now would be the potential for catastrophic engine failure in the event of a loss of meth, be it through a pump failure, clogged nozzle, running out of meth or any other potential scenario that could lead to catastrophic engine damage. I need to get with Torrie on that and see if there's some kind of failsafe device that would detect a loss of meth and pull timing or otherwise somehow prevent a situation like that.