Tapping into a single cell from a LiPo stack seems a very bad idea.
It could kill the stack or the charger quickly.
Use a car charger with USB socket, and plug the USB lead from the Mega into it.
That also will also cut current use from your 3-cell LiPo battery in half.
The 3.3volt output from the Mega (~150mA) might not be strong enough for the Mp3 player + speaker.
But I think that module can also run on 5volt.
5volt through USB is limited to 500mA. The Mega uses ~70mA of that.
Leo..