Two of the claims are unproven; the Affirmative Action claim, and the Pell Grant claim. However, the Pell Grant claim is most likely true, and even if not the fundamental point remains true. As your link points out, Carson received a variety of grants and aid to pay for college. Pell Grants are the first line of financial aid a person receives. Even if it is not true, the essence remains established; Carson received assorted assistance to help pay his education. Whether it was Pell Grants or Lollypop Gild grants, it doesn't really matter.
The Affirmative Action claim, thus, is the only one that can not be demonstrated to bear water. Your link finds no evidence to support or deny, and there is nothing I can see from which to logically infer it. I suspect that someone made a ridiculous assumption based. If there's someone here who has actual knowledge of Yale admissions practices of the time, perhaps they can shed some light on whether it is possible, or perhaps likely, that Carson gained admittance due to Affirmative Action. But as best I can tell, there is no factual basis to justify that inference.