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In the case of the Federal Reserve's biggest categories it works like this. 3.0 trillion - Other deposits held by depository institutions - the banks park almost all of their money (daily) here with the Federal Reserve in order to earn 3.75% and they could drain this very quickly if they needed to do so

Right, so when a bank parks its money at the Fed and wants to get it back, why do you feel the Fed can't make good? When a bank gets it back, where does it go?

2.6 trillion - Reverse repurchase agreements - essentially the derivatives for the securities held & much the same like the 3.0 trillion in being drainable very quickly

You must have reverse-repos confused with something else. When the Fed wants to drain overnight cash from the banking system, they exchange some Treasuries for cash. The next day they return the cash and get the Treasuries back. Why do you feel the Fed can't make good?

2.2 trillion - Federal Reserve notes - if everyone spent their notes or deposited them at the banks & the banks traded them in to the Fed for electronic funds then this would be drained very quickly too.

If everyone spent their notes, why does the Fed notice or care? The Fed can't provide electronic funds? Why not?

0.5 trillion - U.S. Treasury, General Account - this account goes up and down depending on when tax revenues & other receipts come in, outlays go out, and Treasury Notes/Bonds are issued, mature, and interest paid. This could be drained very quickly too.

This is the US Treasury's checking account. When they buy a tank or send a tax refund check, the money comes out of this account. Where could that money possibly go that the "drain" would matter to the Fed?

I have direct deposit for my tax refund. The Treasury account at the Fed drops, the account of my bank at the Fed increases. How is the solvency of the Fed impacted?

If there was a run on the Federal Reserve then the most likely scenario would be that they would turn on the printing presses quickly by lowering interest rates dramatically and buying up lots more Treasuries/MBS.

What does a "run on the Fed" look like?