What Dave said. The BECs in the ESCs power the internal parts of their ESC and, via the red wire, the receiver and anything plugged into the receiver. Two BECs into one power rail might not play nice, so disconnect one.
Both small switches will need to be "ON" for the circuits to work, but both need to be "OFF" when the system is powered down if the battery remains connected. A good idea is to mount them both together so that you can see that both are off. I've been caught by a black switch hiding in a dark recess resulting in a mysteriously flat battery before.