FFT for cos+cos
Hi,
First of all, to clarify, we are talking about the Fourier Transform, not FFT. FFT is a discrete-time transform that may yield entirely different results based on the frequency of the cosine function and the sampling frequency.
Now, regarding the FT of a cosine function, it is two delta functions, one at f0 and one at -f0, multiplied by 0.5 each. For cos(2*pi*2f0*t) the delta functions will be at 2f0 and -2f0 and they will still be multiplied by 0.5. The scale rule you pointed out is correct, but for integrable signals only. The cosine function is not integrable and the FT for it is generalized.
Finally, regarding linearity, you are correct. The FT of a sum of functions equals the sum of the individual FTs.