Money supply - the US Treasury and the Fed

I have been trying to wrap my pea-sized mind around money supply and the interaction between the US Treasury and the Fed, and come again to you all humbly seeking guidance.

a) When the Treasury issues debt and investors purchase the new issues, does that affect money supply? I read an article from the Hussman fund (http://www.hussmanfunds.com/wmc/wmc071217.htm) that says that the new US Treasury debt cancels out any liquidity that the Fed can provide by purchasing Treasurys. However, I have also heard that Treasury issuance by itself should not affect money supply. Does any of you know what exactly happens when the Treasury issues a security? I have a few guesses but that would probably just confuse things.

b) I have also been wondering what it means for the Fed to be constrained by its balance sheet. Let's say they have only $300bn of high quality Treasurys left. Would it be correct for me to think of it as, when the Fed needs to provide liquidity (through TAF, CPFF, or whatever other program), they will sell their Treasurys and use the cash to provide said liquidity? And that implies that the Fed does not want to just print money, i.e. the Fed wants to keep the Fed Funds Rate where it currently is? A followup to this (and does not need to be addressed here if already too many points) is how the Treasury's recent facility (whereby the UST issues debt and simply keeps the cash at the Fed) relate to all this?

Thank you for all your help. A lot of stuff to learn for me, but all of it very interesting.