I have a 3.8v / 3100mAh battery from a galaxy note 3. Can I use this along with https://makersify.com/products/adafruit-powerboost-500-charger-rechargeable-5v-lipo-usb-boost-500ma?
Theoretically you can, but due to the voltage curve over power dispassion when your say 20% into the battery it won't be 3.7 or 3.8 volts it's likely to be 3.5 which is too low to run the Pi, at which point the Pi will shut down. Furthermore the Pi needs more than the 500ma that the power boost offers and may have stability issues, depending which Pi you have. You may read more about Pi power requirements here