No.
Not for Orthodox Jews, but the other branches of Judaism allow it.
Bury them
In Reform Judaism, cremation is permitted but traditional burial is strongly recommended. This violates Orthodox Jewish teachings which hold that burial is required.Read more here at the Reform Movement's Website.
Some secular and Reform Jews think that cremation is acceptable.
Orthodox Jews don't allow men and women to dance with each other, but all other Jews do. (Orthodox, while separating based on gender, do dance, but only with people of the same gender.)
Orthodox Jews don't allow it, but the other branches do whatever they want!
Yes, but Orthodox Jews don't allow women to sing in front of men.
No.
Yes, non-Orthodox Jews can become Orthodox by becoming more observant. Non-Jews can become Orthodox Jews through Orthodox conversion.
Generally, Orthodox Jews are those who have not accepted any of the changes made by the various streams of liberal Judaism. The most visible differences have to do with the roles of women. Orthodox Jews generally separate men and women in worship and do not allow women to lead prayers when men are present. All streams of liberal Judaism today allow ordination of women and generally allow mixed worship. There are different prayerbooks used in the Orthodox world, and some of the liberal prayerbooks differ in only small ways from one or the other Orthodox prayerbooks. Some liberal prayerbooks, notably in the Reform and Humanist movements, have differences big enough for non-Jews to notice. Finally Orthodox Jews have the most stringent standards for who is a Jew, rejecting most converts who converted under liberal auspices. Even the most Orthodox Jews, however, accept that most liberal Jews are Jewish, just not very observant.
Orthodox Jews are strictly observant. Hassidic Jews are even more strict.
Orthodox and Ultra-Orthodox Jews are strict followers of Jewish law.