So, I'm new here and I don't know if only males can be put up to breed, but I think if that isn't the case then the gender should be specified in the dragon's information :)

You should ask this question in the "Help" forum first.

You can breed and request any gender. I just requested a breeding with my male gryphon and someones female gryphon. Just click "breed request" on the females page.

Males can be put up for stud. In a real life situation Males are the one that is usually advertised... You can search for females in "Search" just below the menu. I suggest you ask the owner first on what would be a reasonable offer (or see if it is in their profile) and if they are even willing to breed. The user requests a breeding and the offspring is sent, but you have to request it.

If you mean having the ability to put females up for a reverse breeding and have a fee for them... I don't know. While I support the idea I am tenative because people may not want to breed a female as much as they have less breedings than males.