Yes and no. Let me give you an example: if 70% of Americans get $40K bonus per annum from the fed, it will lead to inflation. However, if the same amount of money (70% of 300M times $40K =8.4T) is given to ten billionaires, it won't lead to inflation.
There are second order effects: if billionaires start buying stocks, thereby increasing the value of RSUs that tech employees hold, this can cause inflation in housing prices.
Yes, but the pressure to pay off those bonds would be deflationary, so in order to sustain the inflation next the Fed would have to do something even more extraordinary! AFAIK this policy pathway leads ultimately to bond forgivenesses (or funky bankruptcies) that eliminate deflationary pressure but may well have the unpleasant side effect of radically adjusting the fiat currency system.
How do you mean? If the Fed creates new money and buys bonds with it, the Fed can continue to hold them forever (really just until they mature) if it wants to. Then the Fed is more or less part of the government, so when the bond matures the Fed takes the bond to the treasury which gives it cash, then it gives the cash back to the treasury. It's like the bond evaporates into nothing when it matures while the Fed is holding it.
If the Fed theoretically bought all the bonds then it could obviously no longer increase the money supply by buying bonds, but we're a long way from that, and even then the Fed could still create new money and give it directly to the treasury to spend in lieu of collecting taxes. Or in the utopia where buying all outstanding government debt and funding the entire federal budget out of new money still hasn't caused the desired amount of inflation, to use to enact a negative income tax.