Almost every single phone out there is capable listen on standard radio frequencies. It depends on the manufacturer whether or not this functionality is enabled though.
I've had three phones where I could listen to the radio -- all three required headphones, so the cord could be used as an antenna. (On my Sony Z3, the "FM radio" is on my home screen; if I don't have headphones plugged in, it displays an "Insert Headphones" message.) I guess you could plug a speak into the headphone jack.
Yeah I heard about that. I tried the Next Radio App, but it said it wasn't supported on my device. Waking up to the radio is a good solution too. But hopefully you'll like the music on jolt enough to keep coming back.