1. The Tenth amendment says the Feds must have Constitutional justification for what it does. It does not specifically limit government powers, but just emphasizes that the Feds have no more jurisdiction than the Constitution says. The Supreme Court was acting according to this.
2. What the Executive branch argues for public consumption does not affect the Supreme Court's interpretation of the Constitution. The Supreme Court has ruled that the ACA penalty is a Constitutionally permitted tax.
A. "Origination" is a slippery word. Not having read the ruling, SCOTUS may have found a corresponding origination in the House.
B. Ah, another idiot who never heard of the Sixteenth Amendment. That one allowed the income tax, among other things. It was passed specifically because, before its enactment, a US income tax was unconstitutional.
C. Who cares about the jurisdiction of the suit? Whether or not the suit was properly brought, the Supreme Court has ruled. It is hardly likely to change its rulings and reasoning if another case is brought. As far as still having a case, yes, they can bring another suit, but it will almost certainly be decided the same way, assuming the Supreme Court hears it.
Frankly, I trust the Supreme Court over a guy who argues the constitutionality of a tax without considering the Sixteenth Amendment.