Sweet dude. What is the maximum milliamp-hours you can charge with this charger?
Zero
Pin 2 of U1 is VSS, and is connected to nothing.
All of your traces there are 4mil, most fab shops will do 6mil minimum, and for power traces even 6mil isn't going to cut it. Those all need to be much wider, even to the point they're larger than the pads they're connecting.
LED has no orientation marking.