The daily/monthly figures referenced are the actions that the Fed is engaging via the Temporary Repo (Repurchase Agreements) market. Hence, they (The Fed) enter the markets, PURCHASE Treasuries from the Treasury and add Liquidity to the system. Conversely, if the Fed were SELLING Treasuries, it would serve the exact opposite purpose and in effect, tighten/restrict Liquidity within the monetary system.
As far as your question, " When the Fed bails out the market on a daily basis, where does the money come from (i.e. do they just print it out of thin air?) and does that money then get added to the national debt which gets passed down to us?"
With respect to the "bailing out" of the markets, please reference the following:
Executive Order # 12631, otherwise know as the "Working Group"/"Plunge Protection Team" (PPT).
Any and all monies borrowed by the Treasury from the Fed are not necessarily "Printed" (a term often used to describe these actions) out of thin air, yet are created with the stroke of a keyboard "Out of thin air" by the Fed itself.