Without arguing your point that morality derives from a higher authority, with which I agree, it isn't correct that those who find the theory of evolution believable must therefore also subscribe to the horrors and deviancies you have listed. That is where the God given ability to choose morality comes in.
No, but the converse (switching precedent and antecedent) is as true as the sun rising every day...
The perpetrators of the horrors and deviancies listed find the theory of evolution believable and also used it as an excuse, as do their enablers who look the other way... they are indeed on the same path...