For conversion to Judaism, consult your local rabbi. Because there are different branches of Judaism, you must learn enough about what distinguishes them before you begin formally pursuing conversion under the auspices of one of them. Note that conversion to Judaism is not quick and easy under any branch of Judaism. Typically, it involves a long period of supervised study, including regular attendance at Jewish services, plus appearance before a beit din (a Jewish court overseen by 3 judges). If you are a man, circumcision may be required, and at the end of the process, after the beit din approves your conversion, you will probably immerse in a mikvah (a ritual bath) to complete the process. You'll be warned that Jews do not believe that conversion is required to be seen as righteous in God's eyes, and you'll be warned that, by converting, you are exposing yourself to potential attack by antisemites.
According to Jewish law, a Kohen can't marry a convert to Judaism.
He didn't.
Nothing. Jews do not seek converts. If a person wishes to convert to Judaism, they are permitted to do so, but Judaism teaches that Judaism should not be proselytized.
No, Obama is a Christian.
yes
Yes, according to tradition.
Only Judaism
His father is a convert to Judaism and his mother is Jewish.
A new Jew.
Lots of reasons. One is that Judaism doesn't believe in encouraging people to convert. If someone wants to convert to Judaism, they're welcome to (although discouraged at first), but Judaism has no mass programs to get people to convert. Nor did it usually have forced conversions like the other religions did. Another reason is that Jews have been heavily persecuted over the years and many were killed.
His father is Jewish and his mother is a convert to Reform Judaism.
Jewish people would call it apostasy.