Yes you should ask for child support if you need it.
Let the courts do their thing and you will have an agreement in due time.
In the meantime, usually courts will give a schedule of visitation. Set up one yourself now. "Hey, babydaddy, you can see her on Wednesday from 4-6 and on Saturday from 10-2. You can call between 5-7 to say goodnight on the other nights. Period. " ...or whatever you feel is right. IF HE IS DRINKING at all - the visit or phone call ends immediately. Put him on speaker.
Until the court has its say, you are tasked with keeping a schedule for your daughter and sticking to it. He is pulling your strings. You are allowing it. Classic dance. Sit this one out.