The President's entire executive branch has been sent home without pay (yes, they got back pay eventually but contractors often didn't) a few years back by Congress. His appointee to the Supreme Court was blocked very effectively by that same body. His trade deal (TPP) is likely not going to be approved thanks again to Congress.
Also, while the justices need the President's help to get onto the bench, they do not need it in order to stay there. This is an important distinction.
Only thanks to the US's Electoral College system, otherwise she would have been President. The matter of fact is that more Americans have voted for Hillary than for Trump.
And going back to the US President's powers, as far as I know the last few wars in which the US has been involved happened without the preliminary Congress approval. Starting a war without the Congress's/Parliament's approval is a royal prerogative since at least the Middle Ages.
> Russia is a de facto monarchy,
Russia is a light-ish dictatorship (people are not sent to the Gulag, yet) which might turn into a tyrant regime (assuming Putin keeps his power and goes crazier), I wouldn't call it a traditional monarchy.
> the United States is a Republic in every way that matters
The Roman Senate survived until at least 400CE (or around that time), meaning 4 and a half centuries after the "de facto" disappearance of the Roman Republic (even more if you go back to Sulla). Thus means that the fact that the US Congress is still around and from time to time likes to play contrarian games doesn't actually mean that the US Republic hasn't lost its original "status" (not an English native speaker, maybe I'm wrong on this word).
Otherwise I can't understand how Obamacare has stood up against the Republican Congress's will.
> His trade deal (TPP) is likely not going to be approved thanks again to Congress.
Had Trump been pro-TPP (or pro-foreign trade in general) I'm 99% sure TPP would have been voted in.
The popular vote is frankly irrelevant because no one was campaigning for it. It would be a totally different game, from the primaries through the general election, if the presidency was decided by popular vote. Republicans would campaign heavily in California and New York. Democrats would campaign heavily in Texas. Drawing any conclusions from the popular vote when it doesn't matter is futile.
Google the word "filibuster" and you'll have your answer. The Republican Congress didn't have the votes to change policy, so they weren't able to. Whether they do now is actually a matter of some debate.
> Had Trump been pro-TPP (or pro-foreign trade in general) I'm 99% sure TPP would have been voted in.
I disagree, but that's beside the point. It would only get voted in if the Congress decided to do so. That's the crux of my argument; policy gets made by Congress and enforced by the President. Trade deals get negotiated by the President and then approved by the Congress. That's the design, and also how it actually functions.