We’re having a big problem in America these days, with the forces of antireality on the march to deceive our children. Evolution is a big target for them, of course, and I need not belabor the battle here. 
Once upon a time, in vague exasperation at a persistent creationist, I opened up two of his questions to the Pharynguloid horde in a contest to see who could answer them most clearly and succinctly. I shouldn't have done this; I'm lazy, and this was too much like grading term papers. Still, there were a lot of good answers, so it was a worthwhile effort.
The winner, judged for clarity, brevity, and accuracy, was Calilasseia, an infrequent commenter here who clearly needs to increase his or her frequency. I've sent off an email in hopes of a reply with a mail address, or if Calilasseia notices this, maybe I'll be sent one soon. Or not. The Prize in this contest is an appropriate and ironic one: a copy of Slaughter of the Dissidents, by the incredible Jerry Bergman. Only the first volume, though; he hasn't finished writing the other dozen or so he says are in the offing.
I feel a little guilty. That's like going on a game show, picking door #2, and discovering that your prize is a goat. In this case, it's a GOAT ON FIRE, which helps a little bit, but still…I'll also slip in a surprise book of a more worthy nature if Calilasseia gets back to me.
Here are the two questions and the winning answers. I repeat, these aren't the only good answers—go back to that thread and browse and there are plenty of well written short replies.
Was evolution a significant and essential factor in guiding Nazi thought?
No. First of all, as has already been established courtesy of searching through Mein Kampf in detail, Hitler's assorted eructations on nature reproduce well-known creationist canards, including the static species fallacy, and Hitler also asserted that fertile, viable hybrids were inpossible, which is manifestly refuted by this scientific paper (among many others):
Speciation By Hybridisation In Heliconius Butterflies, by Jesús Mavárez, Camilo A. Salazar, Eldredge Bermingham, Christian Salcedo, Chris D. Jiggins and Mauricio Linares, Nature, 441: 868-871 (15th June 2006)
Also, even an elementary search of Mein Kampf reveals the following statistics. The number of instances of key words are as follows:
"Darwin" : ZERO
"Almighty" : 6
"God" : 37
"Creator" : 8
Hitler was inspired by the anti-Semitic ravings of one Lanz von Liebenfels, who was a defrocked monk, and whose magnum opus bore the Pythonesque title of Theozoology, Or The Account Of The Sodomite Apelings And The Divine Electron. This was in effect a warped Biblical exegesis, which rewrites the Crucifixion story, and also contains a mediaeval bestiary replete with instances of Liebenfels' florid imagination.
Additionally, the Nazis placed textbooks on evolutionary biology on their list of seditious books to be burned, as illustrated nicely here, where we learn that in 1935, Nazi guidelines with respect to seditious books included:
6. Schriften weltanschaulichen und lebenskundlichen Charakters, deren Inhalt die falsche naturwissenschaftliche Aufklärung eines primitiven Darwinismus und Monismus ist (Häckel).
Translated into English, this reads:
Writings of a philosophical and social nature whose content deals with the false scientific enlightenment of primitive Darwinism and Monism (Häckel)
The evidence is therefore conclusive. Nazism was not inspired by evolution, and indeed, much of Hitler's own writings are creationist in tone. The Nazis destroyed evolutionary textbooks as seditious (much as modern day creationists would love to), and the Nazi view of the biosphere is wholly at variance with genuine evolutionary theory, involving fatuous views of race "purification" by the establishment of monocultures that are the very antithesis of genuine evolutionary thought, which relies upon genetic diversity.
Can natural processes produce an increase in complexity?
The overwhelming evidence from the scientific literature is yes. Appropriate papers include:
Evolution Of Biological Complexity by Christoph Adami, Charles Ofria and Travis C. Collier, Proceedings of the National Academy of Sciences of the USA, 97(9): 4463-4468 (25th April 2000)
Evolution of Biological Information by Thomas D. Schneider, Nucleic Acids Research, 28: 2794-2799 (2000)
Indeed, in the latter paper, Schneider establishes that selection processes cause the amount of information in the genome to increase to a maximum.
Likewise, instances of this taking place in real world organisms are well documented in the scientific literature. Such as Lenski's landmark paper on historical contingency in Escherichia coli, the literature centred upon nylonase, and the evolution of antifreeze glycoproteins in Antarctic Notothenioid fishes. From the world of aquarium fishes, there is also a well documented mutation known as the double tail mutation, which results in indivduals of Betta splendens inheriting the mutation developing two complete tail fins, a mutation that moreover, obeys single-factor Mendelian inheritance. This constitutes an example of increase in organismal complexity, that comes about as close to realising creationist canards with respect thereto, as any observed instance in Nature is ever likely to.
More to the point, there exist numerous papers covering de novo origination of genes, of which:
De Novo Origination Of A New Protein-Coding Gene In Saccharomyces cerevisiae by Jing Cai, Ruoping Zhao, Hifeng Jiang and Wen Wang, Genetics, 179: 487-496 (May 2008)
is merely one of the more spectacular instances. Surely the emergence of a gene where previously there was none, constitutes an increase in complexity by any reasonable measure? Particularly as the instance in the above paper arose from a previously noncoding DNA sequence?
