There seem to be four questions here. I can't give complete answers for each of them but let me address them in turn.
What exactly is one looking for in audio data to find different instruments or energy sources?
There's not really a single answer to this. There's lots of research into many closely related but ultimately different problems. In general instruments vary in the way their spectral properties vary over time. Tracking the changes of all the harmonic and inharmonic components of a note amongst other sounds is no small task.
So the FFT can extract frequencies, but how can e.g. percussion be detected alongside e.g. a bass line?
Generally you'd use a Short-time Fourier transform so that there's time data as well as the spectral information. From here you've got a few problems to think about:
Source separation: look up techniques such as ICA, NMF and CASA.This will divide up the energy between the detected sources allowing you to detect the separate instruments.
Fundamental frequency detection: I recommend summary auto-correlation of frequency bands rather than purely time or frequency domain methods.
also Source identification (which I don't know much about).
Would the frequency bins be checked into a frequency mapping of instruments? This would lead to collisions in possible instruments.
You need to apportion the frequency information not just assign it all to one instrument.
Are the frequencies of a FFT output directly mappable to pitch frequency charts or should there be a conversion first?
The fundamental frequency, which is given on a pitch-frequency chart, may not actually present in a note ('the missing fundamental problem'). So a fundamental frequency detection algorithm such as the one I suggest above will be needed before you can use the chart.