Thanks Octavio! Great questions:
1) To charge the internal battery you can plug the FED3 in by either microUSB port (yellow arrows below), leaving the battery plugged in. Either port will charge the battery at the same rate, the external one is usually easier to access. You don't have to unplug anything to charge the battery this way. To fully charge the battery through the Adalogger board it will take ~40 hours, although if you purchased from OEPS they added a resistor to cut this down to ~20 hours.
You can also remove the battery and recharge it outside of the device. In my lab we have lots of spare batteries and we charge them outside of the device using this
simple little charger, which can charge it in ~10 hours. The battery is a
4400mAh from Adafruit if you want to buy a spare.
2) The battery life will depend on how it's being used and the task being run. Basically the motor is the biggest power hog so if you dispense more pellets in your task you will get less battery life. But roughly you can expect a 1 week battery life for normal use.
Hope this helps! -Lex