Most low fares require that you stay over at least one Saturday night before your return flight. However, some fares may only require you to stay a minimum of 3 or 4 days. One airline is better than two. It's almost always less expensive to use only one airline for a trip instead of two. Booking two airlines can, in some cases, cost hundreds of dollars more.
Airlines sell only a limited number of seats at the lowest fares.
When those seats sell out, the price goes up. If you don't at first succeed, try an earlier or later flight. To get the lowest roundtrip fare, that fare must be available on both the departing and return flights you select. If the fare is sold out on either of these, the price you end up with will be much higher. You may enjoy significant savings if you are willing to fly into nearby airports.