E-brake switch: check resistance at the switch terminals. It will be either zero or infinite for on-off. Alternatively, use a continuity tester on the switch contacts and look for the light or beep when switch is on.

Radio: almost certainly this is inside the radio: your power is not disappearing on shutdown. The memory module inside the radio is not maintaining the presets. There may be a rechargeable onboard battery that does so, but you won't know unless you take it apart.