Explain the stereotypical fee structure charged by hedge fund managers; try to include all aspects that you can remember?

Describe what is meant by a "13D letter", when an investor must file form 13D, and the type of hedge fund investing where 13Ds are most commonly relevant.

Explain the importance of hedge funds to investment banks, including multiple ways the banks earn revenue from hedge funds, types of business, and which division of the bank is most relevant?

Assume a press release comes out overnight saying Acme Co will buy Widgets Co for $100 per share in cash. Widgets stock opens at $95, up from $80 the day before. A merger arbitrageur believes there is a 90% chance of the deal closing, and that if it doesn't Widgets stock will definitely go back to $80. What trade would they do? Per share, how much profit/loss will they incur if the merger closes, and if the merger does not close? Combining those two potential outcomes, what's the expected value of their trade?