What is the benefit of FFT when we're already sampling at an acceptable rate?
Not all periodic signals are sinusoids.  Items 1 and 3 should not assume such.  Not all sampling is done just for reconstruction.  Look up other needs or uses for sampled signals.  
A linear time-invariant system can behave differently to different frequency sinusoidal inputs (as provided by common solutions to certain low order differential equations), so it may be easier to figure how that system responds to other types of far more complicated inputs by breaking them down into the sum of simpler sinusoidal ones.
A DFT or FFT won't break down a pure (unmodulated) sinusoid that is integer periodic in aperture into other sinusoids (other than that a pure sinusoid of an arbitrary phase can be broken down into component cosine and sine sinusoids of that same frequency).  But an FFT can "break down" other types of signals.