When the FED returns it's profits to the Treasury, what does the Treasury do with it?

Earlier, strat2131 already answered some of your questions, but I will elaborate.

If the Fed sells securities through Open Market Operations, then there would be a monetary contraction of the base money supply, and in general would be deflationary, but this does not happen very often.

In reality, the Fed increases its balance sheet assets (Treasury securities) and corresponding liabilities (Federal Reserve Notes) over time, and thus in general is inflationary.

Here is a link about Open Market Operations:

http://en.wikipedia.org/wiki/Open_market_operations

Here is my explanation about how this works:

[url]Question about open market operations - #4 by Think_Blue]

Then bond prices would fall, and bond yields would rise, until enough buyers are willing to buy.

Let me understand this. The Fed buys a Treasury security directly from the Treasury, and sells it on the open market? Then yes, there would be no increase to the base money supply.

But the Fed usually buys more securities then it sells, so it would rarely reduce its balance sheet assets.

I don’t understand your question.