So are you saying if Kerry had a Jewish Mother and Catholic father he does not have to convert?
If you have a conversion that is halachically correct (beit din with shomer shabbos rabbis, mikvah, and for men circ) you are Jewish according to Jewish law.
The father's religion does not matter. If mom is Jewish, so are her children.
That is absolutely correct. He would be a Jew by birth.
According to the article, the Kerrys' paternal grandparents were Jews who converted to Catholicism. Kerry's father's mother was Jewish, so Kerry's father, according to Jewish law, was a Jew by birth. Since John and Cameron's mother was not Jewish, however, they are not halakhically Jewish.