Properly interpreting FFT output
The upper half of the DFT being the conjugate mirror of the lower half is only true for real valued signals.

For an alternative understanding of what the DFT means you can read my blog article DFT Graphical Interpretation: Centroids of Weighted Roots of Unity.  I also recommend your read my first article "The Exponential Nature of the Complex Unit Circle" for an understanding of the foundation of the DFT, in particular, the significance of the Roots of Unity.

Hope this helps.

Ced