Does the Fourier transform give the frequency response?
The relationship between the impulse response and the frequency response is one of the foundations of signal processing: A system's frequency response is the Fourier Transform of its impulse response.
How does sampling frequency affect FFT?
The amplitude of the DFT (FFT) is proportional to the number of samples. Therefore, if you sample for twice as long at the same sampling frequency, or if you sample for the same duraiton but twice as fast, you will have twice as many data points, and the DFT amplitude will be twice as large. See examples below.