I have since found out that I need a wali for my marriage to be valid, and that I should be married in the correct Islamic way.
I have spoken to my husband about this and he does not want to do this. Is our marriage still valid? And if not, should I separate from him since he refuses this?
Praise be to Allaah.You must convince him to repeat the marriage contract with the proposal from the walee (guardian) and acceptance by the husband. Try to avoid him and keep away from him until the contract is redone, and Allaah is with those who are patient. See also Questions #s 2127 and 6122.