Can you give some examples? Are hedge funds also market makers?
Market Makers provide a service. They are responsible for keeping the market liquid - and the SEC is watching to make sure they do. They sell small quantities of stock and profit off the bid/ask spread. They can do this because they hold a wide array of stocks and have contracts with other firms and access to people on the trade floor. They make money by purchasing stocks from sellers at the bid price, then charging clients the ask price. The difference between the bid and ask price is their commission.
Could most hedge funds do this - probably. Do they all want to - no. It's a new set of regulations and there are already companies in that space. If the hedge fund doesn't have trouble attracting new investors it probably doesn't make sense to enter an already somewhat crowded market.
Now for your question about options markets specifically. Many market makers are already in the options market (links at the top talk about options trading as well). They already have everything they need - stocks and a marketplace. There are far fewer "arm chair" options traders, so the market doesn't get anywhere near the attention.
Market makers tend to be individuals that work for financial institutions such as banks and brokerage firms. They are contracted with an exchange for designated securities (a Designated Primary Market Maker or DPM). Per requirements, he sets his Bid/Ask spread which has maximum limits and he must transact a set number of contracts with anyone willing to transact at his posted prices.
A common misunderstanding is that a market maker sets the bid/ask price and that you must trade at that price. Any market participant can offer a higher bid or a lower ask price than the DPM and become the market on one side of the NBBO quote (you can be on both sides with equities but not with options). If you do so, you are acting "like" the market maker since yours is the best bid or the best ask. Temporarily, you are the market maker (on that side) until you get a fill or someone offers an even better price. If a counterparty is willing to transact at your price, your trade is executed and the DPM has nothing to do with the trade.
Though it's far from complete, here's the CBOE Symbol Directory for equities which lists the name of the DPM.