RE: What is the purpose of the brake on the ESC for
With belly-landed planes (i.e. planes with a prop swing that will strike the ground when landing) you want to stop the prop before you land. With nitros, you just kill the engine and the compression stops the prop (and you try to "time" the prop so that it stops horizontal with the compression). With electrics, unless you have the brake set up, it will still spin after you kill the throttle (from momentum and windmilling). The brake slows the prop down quickly so you are less likely to break your prop when you belly-land the plane.