In first question, we have information how the data is represented while in second question we have information that data can't fit into main memory.
In first question, data is stored in array, so quick sort will be better option than merge sort because quick sort has good locality of reference on the other hand merge sort might be slow because it require extra memory to sort.Therefore quick sort is best algorithm for sorting in this case.
In second question,data can't fit into main memory because of less availability of main memory,so we need some external sorting algorithm(outplace) that is merge sort.