Around the world "liberal" is synonymous with "capitalist". US is pretty unique in that it considers liberalism a leftwing ideology
No longer true; the left wing in the U.S. started splitting from the liberals over a decade ago and that's more or less complete at this point.
Yeah for sure, speaking purely on the American common framing of big L Liberals as akin to social liberals rather than classical/economic liberals.
Left/Right alignment is relative, and the American political center is...where it is, and has been drifting rightward since Bill Clinton's "Third Way".