How can I prove father/child relationship with my dad when I fill form DS-130?

In connection with your first question about proving the relationship between you and your father, the USCIS will require a certified copy of your birth certificate with identification of your parents. Beyond that, evidence of your father's role in your life may include photographs, affidavits, school records, residential leases, etc. In connection with your second question, an adult U.S. citizen may petition for a biological father and the biological father's wife (the step-mother of the U.S. citizen), where both the father and step-mother reside abroad, through consular processing, including an application for the father as the primary beneficiary and an application for the step-mother as a derivative beneficiary. Of course, eligibility involves many items beyond proof of relationship, and the application process can be significantly more complex than it may appear from reading the relevant forms and their instructions. It would be wise for you, your father and your step-mother to consult with an immigration attorney who, after learning all of the relevant details, could advise about eligibilities, options and strategies, and then could offer legal representation in the application process.