carrier frequency difference
1 As defined, the device-dependent fingerprint offset should be constant for a given device so if you have nominal_carrier_freq = 1000; then  you could say 

unique_dev_offset = 1;
unique_dev_carrier_freq = nominal_carrier freq + unique_dev_offset


2 Using the Gaussian distribution is common for modeling any deviation from nominal. Think of the context. Our goal is to have devices that are identical, but in real life they have some slight differences. Take a resistor for example, with a nominal value R. If we have a set of resistors we will see some are a little different than R but the majority of them are centered around R. So our model single modal distribution around R. With decreasing probability of being far away from R. This could be a lot of functions (triangle for instance meets those requirements) but the Gaussian is used because it has nice mathematical properties and usually fits real world data very well

3 I think you have to say the channel is constant for this to work. now imagine we have two signals. both are supposed to be the same but they have some unique characteristics. in the images below, I have two signals, one at nominal frequency (0 carrier freq offset), and one with a nonzero carrier frequency offset. We can see that even after adding noise the signals are still distinguishable from each other. Noise won't affect the characteristic frequency offset of the signals. It may modify the appearance of the signals, but not the underlying characteristics

hope that helps