I don't think the changelings in the Great Link do have a gender identity. This seems unlikely to me, because they don't exist as individuals there, so how could they have gender?
But Odo is quite different. He grew up among people with a strong gender identification, so it seems logical that he would develop a gender identity himself if we assume that we are to a substantial part influenced by our environment, not only by genetics.
Concerning the female Founder - funny to call her that when he haven't even established if she is female - I really think that she was trying to form a relationship with Odo and saw that as the best way. I am also not sure if it was ever mentioned that the Founders were in the habit of taking humanoid form. If they did it very rarely it would make sense that the female Founder would keep the appearance she had taken - similar to Odo - when they met the first time, later when she had to be in humanoid form more often.