Is accelerometer taking as much power (current) as it needs?
I had already used one of those modules. It can be powered with a voltage from 3V up to 5V.

It can virtually work with any microcontroller that have a I2C peripheral.

Be aware that you need to write some values to its configuration registers before you can get any data from it.

The accelerometer reference is MPU-6050, you can look for the datasheet on the Internet. There is one covering the registers and other covering its general characteristics.