Buying at market price means you are agreeing to buy the asset at the price the market is currently settled at. This price changes every second and thus if you are in a hurry to buy because it suddenly dropped a lot crossing your buying point this would be choice.

Comparing to Limit orders, you use the money to start a limit order where the price will be of your choice and the order will remain active till cancelled. The Limit order become a Market order as soon as the target price is reached and is executed then as a Market order.

No, its called order matching. You dont have to worry about that, the exchange will do that for you. Just like you are trying to buy the asset, someone on that exchange is trying to sell it. So when the orders match either partially or fully they will be executed or if not, the program will wait.

I suggest you learn what is trading first before asking the questions.