In a NASDAQ fast market, for instance at 9:31am, is a market order more likely to be filled quickly than a limit order? Even though the limit price is set quite a bit above the current market price. In other words, do market orders have priority over limit orders during fast market conditions? Are market orders filled first, then limit orders.
Market orders have no priority over limit orders for Nasdaq stocks. It is simply price/time. If you trade using DIrect Access and ever use SOES, you will definitely (in my opinion) want to price the order above the offer to buy and below bid to sell. This will keep your place in the SOES queue (time priority) in case you miss a fill at the current inside price.
You have to be careful with "market orders". Depending on your routing, market orders may not even be accepted ! As an example ISLD only accepts Limit orders, but simulates market orders by placing a limit order above/below the market. You also have to understand how your broker deals with the limitations (as just described), time-outs, etc. e.g. if you want to SELL, your software may try to either hit specific MM in turn until you're filled, leave it up to SuperSOES, etc. Make sure you understand all of this before trading "fast" markets. If you need to "panic out or in", the fastest way I've found is to do an above/below order on ISLD. Some of my trading buddies swear by SuperSOES - I haven't used it much.