I have recorded a live choir performance using typical compression parameters. Is there a way to find how much compression was used, and at which points?
(This answer assumes that the OP is asking about dynamic compression while recording)
Note : it is usually considered bad practice to apply dynamic processing while recording as it is much easier to apply dynamic processing in post than to undo dynamic processing on a recorded track. There are nevertheless cases where dynamic processing is inserted in the recording chain, either as a protection over overloads or a way to reduce dynamic range of the recorded signal, or as a voluntary artistic effect managed by a qualified operator.
Is there a way to find how much compression was used ?
Case 1 : you have an unprocessed version of the recording
That is as easy as comparing the two files to check on each sample how much gain reduction has been applied on the processed version.
Case 2 : you only have the processed version of the recording
Given any sample
x from the processed file, you have no way to know wether
x has passed thru the processing without any changes or if it has been subject to a gain reduction.
There are nevertheless some common artifacts to dynamic compression that can be audible. These can be clues of when and how a dynamic processor went into action. As @ToddWilcox has mentioned, the more you are aware of the characteristics of the unprocessed signal, the more you will be able to hear or quantify the effect of the dynamics processing.
We will assume that a dynamic processor is defined by threshold, attack time, release time, ratio. knee is not taken into account.
A common audible artifact is pumping.
pumping happens when the input audio has wide dynamic range or threshold is too low. Some high level input triggers gain reduction in the dynamic processor, and when a quiet part follows, you can hear the background coming up as the gain reduction is released. This can be associated with short attack time, short release time, high ratio, maybe too low threshold.
Another common artifact is overload.
overload is when your recorded signal went over the maximum accepted level. Although you have a dynamic processor in the recording chain, some peaks were too high. This means your attack time is too slow (too long in other terms) and/or the ratio is too low. Actually, a compressor with short attack time and high ratio tends toward a limiter. Using a limiter while recording, especially in situations where you have no overview of what will append in terms of audio level, can be a safety net, if you don't set the threshold too low.
Dealing with live recordings
Try to have some rehearsal where you can anticipate which kind of low and high level you can expect.
You can manually correct the recording level along the show, especially if you are aware of low/high parts in the performance.
If you also have a dry track without compression then yes. You could plot the spectrum (aka fft) of each and look at the difference in level. But you would have to calibrate the levels of the two spectra based on a quiet uncompressed segment of the recording and any particular spectra would only be for a particular moment in time (a spectragram would show you compression over time but it would be more difficult to gauge the levels depending on how you plot things).
If you do not have a dry uncompressed track then no, compression is a one-way function.
No. Don't do that, ever. Compression is for postprocessing: you should never do it when recording since it is usually irreversible. There was some minor point to it in the analog processing domain when recording on analog tape (in fact, Dolby B noise reduction facilitates a mostly reversible multi-band dynamic compression) to get above the noise floor. For digital media, don't do this: the noise floor is fixed at the digitization stage. Just be sure to have enough media for recording in a non-lossy format (such as WAV rather than MP3). Depending on your recording equipment, more costly formats like 24bit and/or 96kHz might be mere window dressing and won't add any additional information actually correlated to the input.