Do market orders only get filled IF there is a buy and a sell market order?

Let's say the market has 3 people trading for a company's stock.

Person one bidding $10, person two asking $11, and person 3 buying at market price.

How will the market order buy get filled?

Now, let's say 4 people:
Person one bidding $10, person two asking $11, and person 3 buying at market price, Person four selling at market price.

The broker will collect $11 from person 3, and give person 4 $10, and pocket the $1. And will move the stock from person four to person three. Is my understanding correct?

Now, for persons 1 and 2, their orders will never get filled unless buyer increased his bid or seller reduced his ask. Correct?