Lipo battery powered UNO : charging and using at the same time


I have a single cell 3.7V Lipo battery hooked up to a 5V step-up converter that goes into the 5V pin of my Arduino. So far so good.

My goal is to use the battery only when there is no external power for the Arduino (USB / barrel). When the Arduino is powered via USB / barrel connector, ideally the battery should be charged via the external power.

So I added this Micro USB Lipo charger breakout. The breakout has pins for the battery (+ and -) that I hookup to the step-up converter.

I have 2 questions with this setup :

  1. When the battery is hooked up to the step up converter and the Arduino is in use I cannot charge the battery through the micro USB port on the breakout. I can only charge the battery when it is not connected to the Arduino. (when there is no load on the battery).

  2. I would actually like to have the battery charge when the Arduino is powered by an external source (either USB or barrel). How would I hook this up ? I'm guessing it's not safe to both input 5V via the battery and also hook up an external power source over USB / DC barrel (as that would also result in 5V being put on the board). Do I need some additional circuitry for handling this ?