Intuitively, what is fourier series representation of a signal? Also intuitively what is frequency response?
A fourier series essentially breaks apart a periodic signal to represent it as an infinite sum of sine waves that are in that signal. So a fourier transform of a signal breaks apart the signal to look at all the frequencies that are in that signal (essentially looking at all the ingredients that make up that signal, ingredients being the frequencies).

A frequency response is the frequencies of an output signal compared to the input signal. Essentially, a measurement of how well the output can replicate the input.