Civil Liberties in the U.S.A., & the Constitution

NO ESSAY required, but I need to know which Amendment to the U.S. Constitution guarantees “fair hearings” and egalitarian treatment of all citizens, and even all those individuals/free agents here on U.S. soil; further, I need the precise names of the two clauses which guarantee same; along with the year, and the circumstances, in which the Amendment was ratified. (hint: My professor is saying that this Amendment has evolved, through the doctrine of unintended consequences, to provide the “Anchor Baby” theory for emerging American families. He says it is also the reason the so-called “worst” of terrorists are held at “Gitmo” in Cuba, instead of elsewhere on U.S. soil). Hope this helps — remember; no essay — just answers. Thank you in advance/