Like Austen said, there are two bolts on the underside of the carb. The one that is right dead center holds the bowl on the carb. The other one that's off to the side is the drain. 10mm wrench fits them both.
With the kind of petcock you have on that mower, if you want to drain the carb of fuel, you'll have to remove either of the bolts on the bowl. Unfortunately, in order to stop the flow of fuel on your mower, you have to turn it off, so there isn't a way to run the carb dry with the engine running.
With the speed control lever on the handle bar fully to the stop position, the petcock should be closed, and the flow of fuel shut off. One way to find out for sure is to take that drain bolt out of the float bowl. If gas stops coming out of the bowl in a short time, the petcock is working just fine.
Whether you can mow in second gear depends on the condition of the grass. Tall, thick or wet grass, maybe, maybe not. You'll just have to try it and see.
Did you get the issues with the transmission figured out?