This should happen only on rare occasions. If you are finding this happens often, first double-check that you are following the rules correctly. If it does happen, do the following depending on which rules you are using.
Basic: Each player gets one more turn (without drawing). Advanced: All players may add cards from their hands to their own collection areas, then the round ends.
You most certainly can. The only requirement to go out is to have five or more complete collections, they can be any kind that you are able to create, even if that means all five are the same kind of collection of the same suit!