A: Yes, it does have both a buzzer and a radio to wake you up.
A: It has both. :)
A: The display is not dimmable.
A: Hi, Beth! Regarding your question about the JENSEN AM/FM Alarm Clock Radio - Black: Yes this plugs in for primary power and has the option of using a battery backup. If you have any additional questions, please do not hesitate to contact MyTGTtech at 877-698-4883 every day, between 7am-11pm CST.
A: Battery Back-up for Clock - 2 x “AAA” Batteries Required (Not included).