Yep, the player should do all that you want. Note that the player cannot be played while being charged by your laptop and using a regular USB cable–but it plays just fine while being charged via an AC USB adapter or a battery charger, or also via your PC when you use a power-only USB cable. (I know that you’re not really interested in the PC charging aspect, but thought to mention this here, to round matters out.)
And the FM radio can be set manually to either mono or stereo.
Go fer it! 
