Am I correct in saying that market orders are matched only to limit orders, and not to other market orders? And related--if no one placed market orders, and thus the bid and offer were never hit, price would never move, correct?
Yes, market orders are always matched with limit orders. Incorrect on the second point, because there are such things as marketable limit orders; example, at 15.35 there are 500 shares on the bid, and at 15.34 there are 1000. If I send in a sell limit order for 1000 shares at 15.25, it will execute 500 shares at 15.35 and 500 shares at 15.34, immediately. If I sent in a 1000 share market order, it would have the exact same function. The difference is, if a flash crash happened and all the liquidity down to 12.00 disappeared, the market order would sell at 12.00 or whatever, whereas the limit order wouldn't execute. Basically, a limit order that takes liquidity and immediately executes against resting limit orders in the book is called a marketable limit order.
Thank you very much for the information--the "marketable limit order" is just a regular limit order though right, not a special order type? In other words, market orders can only match with limit orders, but limit orders can match with other limit orders?
Yes, a "marketable limit order" is a limit order like an in-the-money-put is a put. The marketable part is in the context rather than being coded differently.