How do powering arduino both barrel jack and lipo battery together?
As is described in this post from the arduino forum, There is a MOSFET switch in series with the USB connector +5V input line.  If the battery booster 5V output is connected to the USB input jack, then it will automatically power the UNO whenever power is disconnected from the barrel jack, and will be automatically disconnected whenever at least 7.0V is available at the barrel jack.
If you are experiencing over-heating problems, then you are probably overheating the linear regulator that steps down the barrel jack voltage to 5V.  You need about 7-7.5V at the barrel jack to overcome the 2-2.5V loss through the linear regulator, but anything higher than about 7.5V will just cause the linear regulator to get hotter.