How do I quantify the amount of information being lost by filtering a digital signal?
what metric can I use (or even theory or branch of analysis if the answer isn't a simple one) to determine the amount of filtering necessary?  
  


You can use what you already have, that is, the "strengths" of the components that result from the analysis. You can sort the coefficients in decreasing order and then obtain their cumulative sum. Finally, you can set a threshold and stop adding components once the cumulative strength of the chosen components goes (for example) above 90%. In this way you would be selecting the $N_{sc}$ strongest components and rejecting components that have higher signal-to-noise ratios (or in other words are closer to some background noise level). If this has to be a low pass filter, then after you have isolated the first $N_{sc}$ components that contribute to 90% (for example) of the total signal strength then you can set the low pass filter cut off frequency at the component with the highest frequency (or bin).


  
  For any given analysis window of say 500 samples, how do I determine programatically how to preprocess my signal before trying extract features?
  


Please see previous answer, given the frequency (or scale) limits imposed by the length of the window (here 500 samples), you might have to adjust thresholds and cut offs. Please note that if you try to apply the above algorithm per frame (of 500 samples each), then, inevitably, you will get some sort of modulation between frames which, depending on your application you will have to manage somehow. This is because the signal strength will be changing between windows of 500 samples, which means that the potential cut off of the low pass filter will be changing as well, which means that each frame will bear different amounts of filtering. The easiest way to deal with this would be to increase the window overlap (at the expense of more frames and therefore more calculations).


  
  Given a sample window with a particular spectral distribution, does an optimal cutoff for a bandpass filter exist? (or a notch frequency)
  


Only under specific assumptions about the spectral distribution of the noise. In the absence of this, you can study your signal and try to create a Matched Filter that is tailored to the spectral characteristics of the signal and therefore anything outside that would be filtered out.


  
  if so, does it always exist?
  


Please see previous answer


  
  if an optimal value exists, how do I obtain it?
  


Please see previous answer


  
  What is the relationship between this and the amount of information in the signal?
  


This "Amount of information" is a bit unclear. Information has a specific meaning, so are you refering to the amount of bits that are expected to be able to encode completely your "clean" waveform? Or entropy derived by the spectrum maybe? Or spectral flatness? Or, are you talking about the actual information that this pulse sequence would carry if it was to be seen as a communications signal (?). As a general comment, the low pass filter would lower the entropy of the signal in its output...but this is too general a statement to be useful in your context perhaps (?).

Hope this helps. Happy to ammend the response if more data becomes available.