How to determine minimal detectable acceleration on accelerometer?
Resolution of the accelerometer depends upon the power spectral density and bandwidth. Quoting from Accelerometer Terminology Guide by Freescale semiconductors:


  Resolution: The smallest detectable increment in acceleration. It is necessary to know what the smallest change is that needs to be
  detected. The accelerometer bandwidth will determine the measurement
  resolution, but filtering can be used to lower the noise floor and
  improve resolution further. The resolution can be improved by
  decreasing the bandwidth of the output low-pass filter. The trade-off
  with better resolution is a longer enable time. The resolution is
  calculated by the following equation:
  
  $$R=N\times\sqrt{BW_{LPF}\times 1.6}$$
  
  where N is the power spectral density noise in \$\dfrac{\mu g}{\sqrt{Hz}}\$. he power spectral density noise value is
  characteristic of the accelerometer.
  
  NOTE: If the resolution of the A/D converter is less than the resolution calculated for the accelerometer, then the system will be
  limited by the A/D converter. Otherwise the limitation is due to the
  noise and filter using the equations above.


So for analog accelerometers, R gives the resolution. For digital accelerometers, the resolution of ADC or R, which ever be worse (usually the resolution of ADC) will give the final resolution.