Marriage is not needed to have children as we see in Chronicles I chapter 2 verses 45-49 concerning the children that Caleb ben Jefuna had with his concubines. Caleb ben Jefuna was a righteous tzadik as we see in the Book of Numbers concerning the spies that Moses sent into the Land of Canaan. Caleb ben Jefuna along with Joshua were the only ones who spoke well of the Land, and God specifically praised Caleb that he "went totally with God" וימלא אחרי השם. This is an argument among rishonim, but Ramban brings that in many texts of the Rambam the prohibition of a concubine is missing. Of course there is the need for a natural body of water for purification after the 7th day of the period.  [i.e. it makes no difference if she sees blood for one day or more or the whole seven. After seven, she dips in a natural body of water and is pure. if she sees more than seven that is a zava. If after seven she still sees for 3 days then she needs seven clean days.]