Shortly said, “gain” as a term in music production field means an amount of amplification applied to an audio signal / input, measured in decibels.
When “feedback” as a term is brought in discussion in most of the cases the the reference is that ringing noise (a screeching noise, a squealing noise, etc etc) that appears sometimes in sound systems. It occurs when a loop is produced between an input (for example: a microphone, a guitar, etc etc) and an audio output (for example: the PA System, the loudspeakers).
The calibration microphone is that mic used for measurement rather than recording purposes. These types of microphones usually have a flat response because the main idea is to have a accurate and also uncolored picture of audio source.
In music production field, term “recording” refers to that process of translating information or capturing audio data to a recording format. The data is stored on a storage medium named record or sometimes “recording”.