Pretty sure there are actual laws about public employees accepting bribes ("emoluments"). POTUS is a public employee. We hired him (over my strong objections!), and he draws a salary. In principle, we can fire him, too.

Sure, but the question was about the Emoluments Clause. If you argue that Machado gave the Nobel to Trump in an effort to literally bribe him, within the meaning of 18 USC 201, then that would be a crime. But as with all things, Trump's shamelessness actually works to his defense, here. When there's actual bribery going on, the participants usually try to conceal it. Machado giving Trump the Nobel medal in public in front of the press corps in an Oval Office meeting filled with people in a huge frame and making sure everyone in the media knows about it...makes it a little difficult to argue that either she or Trump thought of it as an actual bribe for which Machado could be immediately arrested.

As for firing him, the President can only be "fired" for cause. And not for any cause - for "high crimes and misdemeanors" only. Unlike Parliamentary systems, the Congress cannot remove him just for doing a bad job. That's a deliberate choice - early drafts of the Impeachment Clause would have allowed for Congressional removal for maladministration, and those were intentionally changed to limit the Impeachment power to "high crimes and misdemeanors." He's a public employee, but he cannot just be fired because we change our minds about whether we want him to be President anymore (as expressed through Congress).