Our constitution does not cover anyone but citizens.
Yes, a president CAN limit immigration for ANY reason.
Look it up.
No, the president does not have the authority to ban all blacks from entering the country anymore than he can ban all muslims. He would have to have the support of Congress and the courts, which would quickly overrule Trump on this.
As I stated before though, this idea would not work from a practical standpoint so it is nothing but hollow, feel-good, rhetoric that will never and can never be enacted.