It’s not a proper noun, and this is HN: pedantry is par. “The president of Xyz” capitalizes the X in Xyz(pn) but not the P in president(n). However, the P in President(pn) is capitalized when it’s a Title suffixed to a Name - but that varies per country by what they title their president-equivalent locally and isn’t always translated, while the concept-slash-role label of ‘president’ in English generally does not (and is often used interchangeably, albeit somewhat wrongly, for ‘monarch’ and other such single-person executive-leader roles). (That we use the same spelling for both title and concept is annoying, as usual :)

Yes. But mostly just because it's in reference to this particular president who's a dullard and displays it regularly in this particular way.