Why is the Anode positive if Anions are negative...?
From Wiki:


  Faraday also introduced the words anion for a negatively charged ion, and cation for a positively charged one. In Faraday's nomenclature, cations were named because they were attracted to the cathode in a galvanic device and anions were named due to their attraction to the anode.


In the diode, and specifically in the so-called depletion region, there is diffusion of carriers (electrons and holes) from one region to the other. Since the Anode is positively doped, it will attract electrons from the cathode, and this will cause the formation of Anions in its side of the depletion region.