No. The Church of Jesus Christ of Latter-day Saints (the "Mormon" church) is not allowed to do door-to-door or street proselytizing as it does in most nations. There are no full-time missionaries called to Israel, and Mormons in Israel may not approach others to discuss religious matters (however they may answer questions if they are asked) The Church does have a handful of small congregations in Israel, and has a BYU extention campus in Jerusalem where students can participate in a special Middle-East study program.
Note that this is an approach chosen by the Church of Latter Day Saints and not on account of any Israeli Law or similar legal mechanism.
If you are referring to the Biblical city of Bethlehem in Israel, yes, there are a handful of Mormons in Bethlehem. Mormons are forbidden from proselyting in Israel, however, so it is difficult for the Church to grow there.
Yes, Mormons are allowed to dance (good, wholesome dances). But they should not be doing any inappropriate dancing.
Yes. Go to Utah and you'll find tons of Mormons that hunt.
They don't. That might be the opinion of a few Mormons, but not most Mormons. The Church itself has said nothing on the matter. Mormons are encouraged to form their own political opinions.
The boy attempted to proselytize his mother into Christianity.
There is twelve oxen in a Mormon temple that symbolic twelve tribes of Israel.
Israel
Yes! Mormons believe in keeping their bodies as healthy as possible - which can include immunization. However, whether or not a child is immunized is at the parents' discretion.
The Church of Jesus Christ of Latter-day Saints (the "Mormon" church) currently has no official policies regarding Freemasons or Freemasonry. Mormons are allowed to be Freemasons and Freemasons are allowed to be Mormons, but Mormon Freemasons are asked to put their religious obligations ahead of their obligations to Freemasonry. For a short period of time, this was not the case, and Mormons were asked to avoid joining the Freemasons and other fraternal organizations.
One of the recruitment techniques of cults is to send members out to proselytize vulnerable people.
The Jewish people used to be called Israel, until the political state was established. You can call them the chosen people, or simply 'Jews', in the same way that you would call Mormons 'Mormons'.
No, Pagans do not proselytize. We believe in free will, and letting people decide on their own on what they want to do/believe spiritually.