Yes, of course.
Yes The brightness of the display may be adjusted to several levels including completely off.
The RCR-20 has 2 Alarm Timers You can wake by Radio, Buzzer with HWS (Humane Wake System) it also has an Adjustable Sleep Timer and Snooze Function
The RCR-20 has a built in AM Antenna and an external FM Wire Antenna. The FM Antenna is "Hardwired" to the unit and cannot be removed or exchanged. In most cases and areas this model gets good reception. If you think you need a stronger antenna please look at the WR-2 or WR-22 which both have External AM and FM Antenna connections.