If it does come down to a "Constitutional question" Obama will almost certainly get to choose the answer since the Supreme Court will not likely accept that anyone has standing to sue except Congress acting under a joint resolution. Senate Democrats will be predisposed to support the president and even some Republicans would rather not risk making Obama's solution a binding legal precedent.
(1) Obligations other than Treasury debt are not specifically addressed. How the 14th Amendment may apply to those payments is not clear. Obama might choose to interpret otherwise but I think it probably it does NOT allow payment in the absence of sufficient revenue or borrowed funds. It only requires payment on actual debt; i.e., Treasury securities, despite the debt limit.
(2) Debt that is retired either by incoming revenue or otherwise under the 14th Amendment can be replaced by new issues without violating the debt limit law so long as the total remains under the limit.