Was a Republic. I think it could be argued that the US is no longer fully governed by the Constitution. The only debate, in my opinion, is when the Republic died. When Nixon killed the last part of the gold standard, unleashing perpetual war, and nearly unlimited funding for the military industrial complex (including the NSA / CIA / FBI) by printing / Federal Reserve financing? The 1930s when FDR massively expanded the reach of the Federal Government? 2001 under Bush? 1913 with the founding of the Federal Reserve?

Yes; a democratic republic, to be precise.

Non-democratic republics include 18th-century USA, where only white male landowners could vote. Democratic non-republics include the UK, which is a monarchy. "Republicanism" and "democracy" are orthogonal concepts.