Regarding the moat, dengue's been a prevalent disease in Delhi for quite some time now. Maybe to prevent the breeding of mosquitoes, they drained the otherwise stagnant water?
Fun fact: You'll notice a small platform in front of the Emperor's throne in Diwane-i-Am. That's where the minister would stand to read out all the cases.
Source: The audio tour I took at the Red Fort recently. It's worth the price.