My father is Jewish but my mother is not. If I had a brit milah or bar mitzvah and converted to Judaism would I be Jewish?
A Jew by birth is only somebody born to a Jewish mother, and your birth to a non-Jewish mother does require you to convert, if you wish to become part of the Jewish people.
The brit milah (and bar mitzvah) in itself is not sufficient as a conversion to Judaism. You would only be Jewish if you were converted by a Beit Din — a Jewish Court of Law, which has the power to officiate over conversions. Of course, if you go through the proper procedure of conversion in a Jewish Court, you would be considered a full Jew, just like any other Jew. You should contact your local rabbinate or Jewish Court of Law for more details.