A handy-dandy quick reference–minor edits and emphases added by me.
“The Fed controls the money supply”: No it does not, it sets an interest rate (what happens after that is up to firms and households and their desire for external funds).
“The Fed injects reserves which lowers the interest rate” or, worse offender, “The Fed injects money which lowers interest rate”. Under normal circumstances (i.e. pre-Great Recession, which is what most people have in mind when saying this), the Fed does not proactively inject reserves, it waits for banks to ask. And, the Fed’s monetary policy never injects money, i.e. never deals directly with the public (M1).
“The Fed printed money during the financial crisis”: No it just credited accounts by keystroking amounts, no Federal Reserve notes were printed. More to the point, none of these funds entered the money supply, i.e. funds held by the public.
“The Fed used taxpayers’ money during the financial crisis”: No it just credited accounts of banks by keystroking dollar amounts.
“Banks use reserves to buy stocks and corporate bonds”: No banks can’t do that with reserves.
“The large inflow of reserves in banks did not lead to inflation because banks did not lend the reserves or based on reserves”: No banks operate that way, bank credit and amount of reserves are unrelated (upcoming posts on this).
“Central banks lend reserves”: No the Fed does not lend reserves because reserves are its liability.
“Fiscal deficits raise interest rates”: No, there was a hint about this in a previous post. More is coming in the next post. (short: fiscal deficits increase productivity instead, up to full employment–zap)