The debt ceiling is a requirement of the US Constitution, so it’s pretty off the mark to compare the US against parliamentary systems that, firstly, are parliamentary systems, and secondly, aren’t subject to the US Constitution.
No, the debt ceiling isn’t literally the USA deciding to order but not pay. The US can, must, and will pay its debts regardless of the debt ceiling. Treasury takes in plenty of revenue to pay its debts regardless of the debt ceiling.
That’s a flat out false claim and we shouldn’t put up with it when politicians start going on about it.
No, the debt ceiling is merely an expression of the idea that the representative branch of the federal government gets final say over whether the whole country will obligate itself to paying back debts.