When we say the govt is printing money, we are not really talking about the paper notes in circulation, rather electronic money (digits in a computer screen) that exists in bank accounts.
Yes, of course. They are not doing that either though.
an excerpt from some quick google search result:
When the Fed creates $85 billion, it uses this money to buy bonds - typically split 50/50 between US Treasuries and Mortgage Backed Securities (MBS). Here is what's important: When the Fed creates and gives $85 billion in reserves to its member banks, it removes $85 billion worth of assets (bonds) from the balance sheets of those same member banks. The result is that no new net financial assets enter the economy.