Yes, it is possible. The requirements are:
1. Convince a rabbi to assist you.
2. 1-6 years of study.
3. Go before a religious court to get approval for the conversion.
4. Go to 'mikvah', a ritual bath (NOT the same as a baptism).
5. Circumcision or symbolic circumcision for men.
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.
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.
Elizabeth Taylor was a convert to Judaism, which dictates that burial occurs as soon after death as possible. You can read more about Bereavement in Judaism, below.
Because Jews are a diaspora that live around the world, and anyone with the dedication to do so may convert.
Anyone can potentially convert to Judaism, regardless of previous beliefs or non-beliefs. The issue is finding a rabbi who will assist the potential convert and the potential convert being ready to study anywhere from 1-6 years prior to conversion. Jews in general have no issue with atheists (so long as the atheist isn't attempting to force their beliefs on Jews).
There are two main schools of thought within Judaism - orthodox Judaism and reform Judaism. Both hold the Torah sacred and follow the law according to Moses, but there are significant differences between the two. Reform Judaism could be considered analogous to progressive or liberal Judaism, in that the Word of God is considered living and to some degree needs to be interpreted with an understanding that several millenia have passed since Moses received the tablets. Reform Judaism follows the requirement for a ritual cut during slaughter, but then allows the animal to be immediately stunned so that it is rendered insensible. There are also differences in the carcass checks that are performed. Orthodox Judaism, in contrast, could be considered analogous to traditional or conservation Judaism, in that the Word of God is considered immutable and transcending the passage of time. Orthodox Judaism follows the exact protocol for ritual slaughter that was practiced in the time of Moses, as it has been passed down from rabbi to rabbi over the centuries. Orthodox Judaism does not allow stunning of the animal after the ritual cut is made and tends to be more stringent in the carcass check requirements. Because there are significant differences between the ritual requirements of reform Judaism and orthodox Judaism, some have criticized the various requirements as being hypocritical. However, this is not a fair criticism - there are thousands of different denominations within Christianity, so it should be expected there are also several different branches within Judaism. Each branch of Judaism will follow their own understanding of their faith and therefore some variation within ritual slaughter requirements should be expected.
Judaism spread fast so equals yes
Conversion to Judaism does not rest on a Zionism litmus test. It does rest on what typically adds up to a year of study under a rabbi, so, as the Talmud says (in Pirke Avot 1:6, in the name of Joshua ben Perachyah) "find yourself a teacher."
A Gentile is, by definition, a non-Jew, so no. Gentiles can take part in Jewish ritual with the exception of ceasing work on Shabbat which is seen to be a Jewish-exclusive activity. Gentiles can study Jewish History, Religion, or Civilization. Gentiles are also free to convert to Judaism if they so desire, but there is no proselytism in Judaism.
Judaism does not proselytize, so it grows only through reproduction and migration.
You cannot convert to Judaism and still believe in Jesus. To convert to Judaism you have to accept the Jewish law and all its 613 commandments - and nothing else. No deviations are accepted. Judaism does not believe in the possibility of a "son of G-d", since in Judaism G-d doesn't have a physical aspect, therefor He can't have any children. Judaism also requires one to worship G-d, and G-d alone without any intermediates. Judaism requires one to believe that the Messiah is on the way; not that he has arrived already.
Judaism didn't help or hinder Hebrew. Hebrew is the main language through which Judaism is expressed. So it's more accurate to say the Hebrew helped Judaism.