A treaty is a treaty. The US Constitution has strict requirements for passage that requires Senate ratification. If it’s not a Treaty then it cannot be enforced if it violates other Constitutional guarantees.
The thread which SisterK references in #10, is about whether the Vienna Convention treaty, which the US ratified a while back, covers subsequent UN agreements. In other words whether, by ratifying the Vienna treaty, the US bound ourselves to treaties formed by the UN afterwards. In my opinion, this would be unconstitutional.
No.
While treaties, properly ratified by the US Senate, can trump law, they cannot trump Constitutional guarantees. Ever.
Only Constitutional Amendments, either via the Congressional/State ratification process or a Convention, can do that.