NEWB ALERT! FFT and band power


I have two rather simple questions about FFT and band powers. I am a newb at this so feel free to hammer it in.

First, I would like to know what data and processing goes into both. Are accelerometer data and blink/jaw clench data used to remove artefacts first before calculating the above?

Second, I am confused about how band powers are calculated in the first place. I guess you need to do a Fourier transform to even get those. That would mean working in the frequency domain, right. How then are time stamps available with the band powers? Is it like putting the FFT of the raw data back on to a timeline. If so what is the time duration of the FFT analysis and how is it happening on the fly (that is at each time stamp)!