Yes, if the parents of the child decide to raise him or her as a Jew, they baby is taken to mikvah as part of the conversion process.
Yes, if the mother isn't Jewish and the parents want to raise the baby Jewish.
The mikvah
a mikvah
In order for a person to convert to Judaism, a person needs to undergo a formal conversion solicited by the convert-to-be (as proselytization is forbidden). The process of conversion can take from 1 to 6 years of study with a rabbi or other Jewish scholar to learn the faith. He must then go before the Beit Din (Jewish religious court), going to mikvah (a ritual bath for spiritual purification), and circumcision for men. Once someone converts they are AS Jewish as anyone born to a Jewish mother.
No, the concepts behind baptism are completely alien to Judaism.
A Jew is someone born to a Jewish mother or who has converted to Judaism; Jewish tradition does not recognize "half Jewish" or "partly Jewish" as a status. You either are or you are not. A Jew who abandons Judaism and adopts another religion is an apostate. It is important to understand, though, that to be Jewish is to be accepted as a Jew by the Jewish community. It is not just between you and God. So, conversion to Judaism involves coming learning enough to come before a rabbinical court and be accepted as a Jew. There are also ritual requirements such as circumcision and dunking in a mikvah. For an apostate to return to Judaism, mere private renunciation of the other religion is not enough, it is also necessary to patch up differences with the Jewish community.
1) Circumcision (for uncircumcised males) 2) Acceptance of the Torah and its commands: to intend to live as a Jew 3) Immersion in a ritual bath (mikvah). In practical terms, the conversion is done with the knowledge, supervision and help of a beit din (Jewish court); and the prospective convert learns about Judaism before converting. Those who seek to become Jewish are (at first) discouraged by the beit din, until and unless it becomes clear that they know what they're doing and are serious and sincere about it.
The main requirement is the acceptance of Torah and the mitzvos (Torah-commands) with the intent to fulfill them. In addition, the convert must immerse in a mikvah (ritualarium), and men must be circumcised. People do not convert on their own; it must be under the aegis of a Rabbinical Beth Din.
The Mikvah is the ritual cleansing of a woman after her period, the reason being that blood is considered unpure and she has just had a period of blood! This article clears up a number of misconceptions about the Mikvah http://tiny.cc/mikvah
There is absolutely no relation between baptism and going to a mikvah.
No, the only Jewish ritual that baptism could be linked to is going to the mikvah because a mikvah is a bath. The meaning behind the two are completely unrelated though.
Yes (Code of Jewish law, Yoreh Deah 201:5).