1 - Noise is usually just that, single pixel standard deviation of output. The normal (and large) non-uniformity of the sensor is of no concern as that is 'the cameras' problem' to sensor manufacturers.
As noise is then divided by response, NETD can be altered two ways; by longer integration at the detector (less mV of noise) or by bias alterations to increase response (more mV per 1°C scene change).
Filters, scene averaging, gamma curves, different displays and colourisation do not change NETD, they change the camera system MDTD. (MDTD = minimum discernible temperature difference)
MDTD is affected by any uncorrected fixed patterns from the camera system.
A smaller aperture lens does not change sensor NETD, as that is quoted at f/1, but it certainly changes camera MDTD.
2 - As bap notes, NUC can be used to mean a full two point calibration of gain and offset, or used loosely to mean for a single point offset only correction. FFC is always just a single point offset only correction - 'flat field correction'.
You'll need to be specific and consistent when referring to these separate functions.
3 - yes several ways, with variable degrees of inadequacy depending on the intended use. Suggest you look out the various patents in circulation.