For part i, I found that the answer is

F(w) = (4sinw - 4wcosw)/w^3

For part ii, I consider

[F(x)]^2 which is equal to 16[(xcosx - sinx)^2]/x^6

and then i tried to use the Convolution relation

[F(x)]^2 = Fourier Transform of [ f*f] = Fourier Transform of (integrate from -infinity to infinity[f(t-k)f(k)]dk)

However, the integration is not converge, so I think there must be some mistakes.

Please gives me some idea on this........