That’s been tried before, and I think historically (and I did take a class on the Economic history), it always leads to hyper-inflation. How crippling it is to the economy depends largely on how fast the country’s fed reserve (or whatever body is designated to control the money supply) reacts fast enough. Often (read almost always), the inflation spirals out of control a state of hyper-inflation takes place. Then, usually, stagflation or deflation results (usually deflation) as a correction. It is much better for the country to simply be more productive and raise their GDP to buy their way out of debt rather than to print their way out of it. In theory, I suppose it could work (with super tight control), but in practice, it never has.
What happens first is that people start investing/or buying because the increased money supply will deflate prices. Then, quickly (depending on how often traded the country’s money/bonds/debt or financial instruments/etc. are traded), economic activity starts increasing (i.e. buying, selling, production, everything that makes an economy move), then as a natural result, inflation increase driving the price of bonds down (this is a lengthy explanation, so I’m omitting because it seems you want the quick and dirty).
[Skipping some important detail] Bond prices drop, investor confidenice wanes, government revenue decreases, price rise, bam - hyperinflation.
That is a correct statement, but it doesn’t show you the whole picture, or really give any knowledge of what is actually happening. For instance, Japan and China buying American securities/debt doesn’t tell you that those two economies are artifically propping up their economy buy keeping the American dollar weak (or, another way to look at it, buy keeping those foregin currencies from rising against the dollar). (This is another long explanation.) Super long story short, buying back the debt would wreak havoc on those two economies and quite possibly cause another worldwide depression. There more also, but I can’t really think of it at the moment.
They are really the Treasure Dept. They issue debt in the form of securities and bonds to make up revenue shortfalls for the government. How that money is allocated is another issue. One with which I don’t have much knowledge on and would be a chore to look up. (OMB might be a place to start).