These are all good points. It should also be pointed out that the Fed is now paying interest on excess reserves, and has been since 2008. This is basically free money to banks who retain extra reserves on their balance sheets. This was put in place to incentivize excess reserves to hopefully counteract the losses on mortgage backed securities until the housing market and wage inflation could catch up with all the money that was printed with mortgages and derivative securities between 2001 and 2007. Unfortunately everyone was caught somewhat unaware, because while it seemed like inflation was low, it actually was too high. At lot of it went into the oil markets as well. What the Fed is doing now is simulating low inflation by having a sort of reverse black hole of interest on excess reserves. They are going to track that up as they raise interest rates and that will give them a new tool to control the money supply. Lower that rate, and the banks will have to invest it elsewhere, stimulating investment. All of this is only necessary because Congress won't increase government spending, which has been the traditional way we've gotten out of these things.. We needed more like a 10T stimulus to really fix stuff..
That's not a good tl;dr. The Fed only controls monetary policy and does not affect fiscal policy, which is Congress' responsibility. The Fed is doing a seemingly good job with the only tools available to them.
