If they did would you agree that such actions were constitutional via treaty?
its an open question. The USSC has never actually ruled on the issue though it is a well established principle that Treaties carry the force of constitutional law. So could the US government agree to a treaty that contradicted and thus rescinded a constitutional right like for example, a UN treaty severely limiting private ownership of firearms? Open question. Very troubling but there is no ruling or precedent saying they can't do this. Just as there was no ruling or precedent saying the Confederate Government could not have done this wrt a treaty that would require the CSA to abolish slavery.
Sure they have. Bond v. United States in 2011 is only the latest. Treaties can have the effect of federal law, but like federal law they cannot supersede the Constitution.