Power spectrum of a pure sine problems
Since FFT treats the signal as if it is periodic you need either to apply a window function (for example hanning) on your signal or make it coherent. In the image3 you attached you may make it coherent by only using data for a number of cycles; use samples 0..31 or 0..63. If the signal is non-coherent it will be seen by the FFT as a concatenated signal with discontinuites that will cause overtones. 

EDIT:
A coherent signal may be concatenated with itself without generating any discontinuites.  

The blue line is the input data to FFT

And a non-coherent: