For question 6 see the attachment for a sketch.

As the function is continuous the cosine series converges to the function values at the three points specified.

The odd extension is f(x)=4-x^2 for x in [0,2), and f(x)=-(4-x^2) for x in [-2,0), and this is repeated in [2,6) and [-6,2) to give the periodic extension.

RonL