Darwin definitely believed in natural selection, but he never used the term "survival of the fittest," nor put it forward as a scientific theory. If you dispute that, cite the relevant passage in any of his works.

"Species evolve without the assistance of others of their species."

Not only do you not understand Darwinism, you don't understand basic biology. It's impossible for a species to evolve without individuals cooperating in reproduction and rearing of offspring, just for starters. I didn't say that species don't evolve if the individual members of the species don't cooperate. I said that species where individual members cooperate have an evolutionary advantage over those that don't.