Bad idea from the start. A UNO is a particularly inconvenient form factor. A Nano is far more sensible. But.
A 3.7 V LiIon battery is not particularly suitable for a 16 MHZ Arduino such as a UNO or Nano. Boosting it to 5 V with a boost converter is not the best of ideas; you would be better to use an 8 MHz Pro Mini and connect a USB adapter when you need to interface to a PC.
Point is that having the USB interface on the battery powered system wastes power. You probably want to put it to sleep to conserve power when nothing is happening.
Just use the proper "5V" pin if you must do it that way. Disconnect it when using USB to connect to a PC.
Even more ridiculous and confused. Don't use "Vin"!
Maybe it will, but if you want people to see it, post it on the forum here.
Maybe read the instructions?