So, assuming Congress doing its job properly, would there be a legal basis for conviction of impeachment? I know you can impeach a POTUS for just about anything, but the Senate has to have an actual trial presided over by a SCOTUS justice. I'm assuming that there has to be actual law, in that case, and not just politics. Yes?

On this one, I would say "no."

I mean, there's a certain argument that there's never any "legal basis" for impeachment, in the sense that it's essentially a political - not a judicial - act. It is available for "high crimes and misdemeanors," but there is no body of law that defines what those things are, no required legal process for any of it (Congress can do what it wants, and need not adhere to any rules of procedure or due process at all), and if they were to convict a President of something wholly unsupported by the Constitution there would be no way (and no one) to gain say it.

Leaving that aside, I don't think that your original question poses a "high crime or misdemeanor." Violating the Constitution is not a criminal act. It is not a criminal code. Presidents constantly violate the Constitution - I don't think there's been a President in recent history that has never lost a Constitutional case in court. If the President ends up doing something that's later found to have violated the Constitution, he hasn't committed a crime (unless it's also a violation of some provision of a penal code).

So violating separation of powers (ie. infringing on Congress' authority to declare war) or going beyond one's enumerated power (ie. using military force in contexts that go beyond the Commander in Chief role) might be unconstitutional, but they are not criminal. And I believe that the term of art, "high crimes and misdemeanors" was intended to cover cases that are exactly that - actual crimes - and not intended to encompass non-criminal disputes between the branches over their respective spheres of power or allegations of maladministration.