How does the Federal Reserve control the mosey supply in the american economy?

The Federal Reserve conducts monetary policy by changing the interest rates. Higher interest rates decrease the money supply throughout the country, as it becomes harder to obtain money due to the fact that it is more expensive to borrow. The opposite holds true for lower interest rates.

When is it more beneficial to obtain financing for your company through debt as opposed to equity?

It would be more beneficial for a company to obtain financing through the debt market as opposed to the equity market when the company is just starting off and will have a low valuation - meaning they would need to give up a large portion of their equity in order to receive the financing necessary.

When a company reports a substantial dollar amount of goodwill on its balance sheet, why should an analyst be skeptical?

Goodwill is an intangible asset that is difficult to accurately put a value on. Also, if there is an event that reduces the value associated with the company's reputation/goodwill, the value will be written down and is not possible to be recovered.