When did Barack Obama pass a same-sex marriage bill?

Answer 1

No, he did not. To do so is outside of the scope of his authority, unless both houses of Congress pass a bill prohibiting states from discriminating against same-sex couples in the issuance of marriage licenses. So far this has not occurred. But perhaps you are thinking of the June 2013 Supreme Court ruling that struck down the Defense of Marriage Act. But President Obama did not bring that case. Plaintiffs from several states (including New York and Massachusetts) sued to overturn DOMA, and in the end, the Supreme Court overturned it as a discriminatory law; at this point, regulation of marriages has been returned to the states, since there is no national law.

Answer 2

He has not, as of yet. He can only sign into law bills that are first passed by the Senate and House of Representatives. They haven't passed a bill on same-sex marriage since 1996, when they passed a bill banning federal recognition of same-sex marriage.

Answer 3

No. The Congress has not presented him with any to sign or veto. The only US president to ever sign into law an act dealing with same-sex marriage was Bill Clinton in 1996.