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Suppose that person A places buy market order with quantity 1000 of firm XYZ. Now in the market there only are various asks of quantity: quantity 100, quantity 2000, quantity 1000. Each ask has different ask price. But the lowest one is $11.00 that has quantity of 100. In this case, which ask will be executed for person A?
Also what if asks do not have ask with quantity 1000? In this case, what will happen?
I assume that there is only one bid for this stock in the market.
I am assuming that you mean in your first question that the lowest ASK is $11, so lets assume a book that looks like:
A $11.20 2000
A $11.10 1000
A $11.00 100
A market BUY for 1000 shares, also assuming the above book were normal orders (not all-or-nothing or having other variant tags), would take out the 100 at $11 and then 900 of the second level - if that was an amalgamation of several orders, then in time-priority sequence.
The second question - what happens to a market order if there is not enough depth of book - will depend upon the exchange rules - and they may vary so you should check. The remainder of the order might be cancelled if it is unexecutable. On the other hand, it might sit on the book, and therefore automatically fill any incoming ASK at whatever price that ASK comes in - which might well be quite far away from what was last traded.
An example of the exchange rules governing execution of limit orders is NYSE-ARCA's rule 7.36.
