The 14 Amendment question is tricky. Presumably the issue would arise if the country was about to violate the debt ceiling and the President ordered the Treasury Secretary to issue new Treasury Notes and Bonds. If the financial markets believed that the new debt had the same full faith and credit guarantee of existing debt, they would buy it; if not, they wouldn't. The 14th Amendment's statement that the validity of the debt "shall not be questioned" suggests that even if the new debt exceeded the debt ceiling, it would find a market, but that's far from a sure thing. And the new "14th Amendment" debt would very likely carry a much higher interest rate than the old debt that didn't breach the debt ceiling.
My guess is that the market response, rather than any legal theory, would determine the status of the new debt. If the markets bought it, even at a higher price, the practical reality is that the debt ceiling limit would have been nullified.
FYI, the Supreme Court has scheduled 2 days of hearings on the California Proposition 8 case and a related case challenging the Constitutionality of the federal Defense of Marriage Act. But I assume you meant to say that the Court would uphold Prop 8 and DOMA.