battery rechargement system
The charging current to the battery will be partially stolen by the MCU and sensors. You have to decide whether the MCU steals too much or, that what is left is enough to keep the battery floated without slow continuous depletion leading to eventual battery failure.

If you think that might happen, you will need to disconnect the load (MCU and sensors) before this occurs and let the charger put all its charging current into the battery.


  Can this component also control the flow of current when the
  microcontroller is being powered by this battery and be charged at the
  same time or do I need another component for that?


You will probably need a comparator circuit that monitors battery voltage level and disconnects the MCU before that voltage gets too low for the battery.