The answers to both, by a 6-3 margin on the Court, were NO. Medellin could not obtain a new trial because of the Texas police's failure to notify the Mexican consulate (as Andy McCarthy noted, under the Vienna Convention on Consular Relations, police in the United States have no obligation to contact the Mexican consulate due to the nature of the obligations assumed by the US and Mexico under the Convention -- remember, international treaties are generally binding on nations to the extent that they choose to be bound). The consular notification was not an individual right granted by the treaty; instead, the treaty created diplomatic rights between the participating nations, which could be made individual rights by legislative action.
The ICJ also had no authority to bind the various states because its jurisdiction is only over the nations that bring a dispute before it and agree to be bound by its decision. Thus, Pres. Bush sought to force compliance with the ICJ's decision through an executive order. The Supreme Court (with all nine members in agreement on this point) said that the President could not do so because the Executive's powers to make treaties did not allow it to impose legal duties upon the states to comply with those treaties -- only Congress and the President could do so through lawmaking processes.
The WSJ touts the ruling as a victory for the US Constitution because:
Chief Justice John Roberts, writing for the 6-3 majority, ruled that the ICJ finding was not binding because the Vienna Convention is an understanding between governments, a diplomatic compact. It was never intended to automatically create new individual rights enforceable domestically by international bodies. Texas's violation was of diplomatic protocols, and calls for a diplomatic remedy.
Treaty obligations, in other words, do not necessarily take on the force of law domestically. Rather, Congress must enact legislation for whatever provisions -- such as consular notification -- that it wants to make the formal law of the land. This distinction matters because it establishes a fire wall between international and domestic law. It also protects the core American Constitutional principles of federalism and the separation of powers. As Justice Roberts points out, the courts must leave to the political branches "the primary role in deciding when and how international agreements will be enforced."Bush's first Supreme Court pick has enhanced the President's legacy.