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What is the red board with the USB connector? It doesn't seem to be mentioned in the parts list.
The battery can be any kind of 4.3V lithium ion battery. I did not go into detail about connecting the Wemos to the accelerometer because it will depend on exactly what hardware you have. In all cases it will be simply wiring the 3V and GND lines, plus the SDC and SCL I2C lines. The ESP32 allows you to configure which pins you use as SDC and SCL which you can see in the code.