I've heard the rumors of having to kill puppies or castrate orphans. Is their is any validity to any of these brutal training tactics? Or just allied propaganda?
Wrong on both counts, I think --
The SS did not systemically kill puppies as official policy. I've never seen allied propaganda against the SS claiming they did.
It is true the Nazi state did sterilize "undesirable" people, such as the mentally ill or disabled. This was a practice known as "Eugenics", based on the theory that preventing people with infirmities from reproducing would eliminate those genes from the population pool of Germany. I'm aware some of the infirm were also deliberately euthanized, under the theory that they were useless bodies consuming valuable food, shelter, and medical resources at a time when Germany had shortages of all of these things due to the war.
The United States, by the way, also practiced a similar program of Eugenics that only ended in the 1970's (the forced sterilization, not the euthanasia). Other nations have at times created similar programs. Such programs are now considered seriously unethical and wrong.
The genetics behind these programs were also unsound scientifically - disorders and diseases that result in mental and physical incapacity can be developmental (caused during pregnancy and childhood), environmental (caused by exposure to toxins or other external forces), and only sometimes genetics. Even some genetic mutations are not hereditary, so much as chance, such as some types of Downs syndrome, which increases in odds of occurring with the age of the mother, although it can happen to any age mother.
All this is in no way to mitigate the crimes and misdeeds of the SS, or make any kind of moral equivalency between them and the United States and other countries.
About those puppies:
Most developed nations have animal control programs that capture feral cats and dogs, particularly in urban areas, but rural ones as well. This is the proverbial "dog catcher", more commonly and accurately called "animal control officer" today.
If these captured animals are not placed with owners e.g. adopted or "rescued", they are typically euthanized (humanely killed, usually with a chemical injection). Some of these animals could be young dogs, puppies.
An excess population of feral domestic animals causes problems on several fronts. The animals are often malnourished, and in their foraging for food may attack and kill valuable livestock, or even attack humans. Breeding populations of feral dogs and cats can damage wildlife populations through excessive predation. These animals can also be vectors for serious diseases such as rabies, and parasites such as fleas and ticks that can carry serious diseases affecting humans.
I'm not aware the SS was ever officially charged with animal control, at least on any large scale.
I hope this puts things in context and perspective.
Eugenics Sources:
Animal Control Sources:
I can't speak completely on specific books that talk about training, however it is my understanding that it was very similar to any other military academy training. War games, tactics, ideological study, etc.
The puppies thing is definitely hard to imagine and I have never seen anything of the sort. Generally speaking, the top Nazi leaders including Hitler himself were very big into animal welfare. There are plenty of sources out there on the party's view on animal welfare and control, and I'd go as far as to say the party leaders at the highest level considered animals something to be cherished on some level. Vivisection were banned to protect animals, and there were some other animal rights laws put into place. Also of note is that Hitler was a vegetarian, though honestly I don't believe it was exclusively based on his love for animals and if I remember correctly was a health issue to him. Still, though I can't think of any specific proof that SS members weren't killing puppies, I find it very difficult to believe that one of the most powerful forces in the Reich with so many direct ties to Hitler would encourage such an act.
hatheaded covers the 'castration' piece. This type of stuff was handled very specifically by Doctors and institutions within the Reich in a very "Nazi" type way (bureaucrats were employed, documentation was drawn up, etc). Not likely this would have been handled as "training" of any sort.
Sources are rough for me as always because I'm not as organized as actual historians here. The only real book I know of directly on animal welfare in Nazi Germany is "Animals in the Third Reich", which I have actually skimmed through during a few 'sit around used bookstore for an hour' trips, but overall it looks like it takes quite a bit of heat for not being properly researched.
Evans's "Third Reich at War" has a very good section on the sterilization and Eugenics programs going on in the Reich.
Maybe doesn't answer all of your "what was training like for the SS" questions, but the assertions being made in your post I'm confident are just that.