In the United States, the 1st amendment of the Constitution guarantees free exercise of religion. Why, then, can't people do whatever they want so long as it is in the name of religion?
The simplest answer is that the free exercise clause does not give you the right to break laws. Such an interpretation is simply absurd and would destroy all sense of law.
What it does protect people from is the government making laws that target specific religions. The government cannot say certain groups of people cannot gather, punish people who do not go to Sunday religious services, or forbid people from wearing yarmulkes, for example.
Situations with Native Americans are complex, and the United States has a long history of making laws (for better or worse) that apply specifically to Native Americans.
The Supreme Court has ruled (Employment Division vs. Smith, 1990) that laws and procedures forbidding the use of peyote are not unconstitutional. The reason that peyote use is sometimes legal is because specific laws have been passed that state it is legal in certain circumstances. Federally, peyote use in the religious rituals of the Native American Church is legal, although use outside of that organization is not.
On its own, yes. There are no laws forbidding the killing of animals in a religious setting. There are, however, laws about cruelty to animals and disposing of remains. These laws are perfectly legal because they apply to every person, not just religious people.
Animal sacrifice is an important component of practices such as Santeria and Vodou, and the law allows it so long as participants follow other laws regarding the treatment of the animals involved. The animals cannot be tortured and must be humanely killed. The carcasses must be properly disposed of, not simply abandoned to rot as is the traditional practice for some rituals. If the meat of the animal is to be consumed, as is often the case, it must meet the requirements of any other slaughtered food animal.
4. Can the government force churches to marry homosexuals?
Absolutely not. Even if same-sex marriages are made legal in all 50 states, this will in no way compel any religious organization to perform a same-sex marriage. Same-sex couples will have the right to be legally married, and that can be performed at a courthouse. They do not have the right to demand a specific person or organization marry them.
This is already the case concerning marriage. No priest, minister, rabbi, etc is compelled to marry anyone. Many churches only marry members of the church. Some churches counsel couples and determine whether they feel the couple is ready for marriage or even an acceptable match. They don't have to give a reason. So if two men approach a church hoping to be married, the church can simply say "no." It's that simple and always has been.
5. Polygamy in the United StatesPolygamy is illegal in the United States. The attempt to be married to two people at once is called bigamy and can be punished by up to five years in prison. Bigamy is primarily a crime of deception, where one person attempts to live two lives with two different spouses without the spouses knowing about one another. It can also accidentally happen if a person doesn't realize he is already legally married, such as a divorce never being legally finalized.
Polygamy, however, is the overt attempt to have multiple spouses. Most commonly it is one man having many wives. Only the person with the multiple spouses is prosecutable; the spouses are not.
However, polygamous communities have started finding ways around the law. One is to act as if married but never actually being married. After all, there are monogamous couples today who live together for years without being married. Another approach is to marry and divorce multiple women sequentially. These practices do not always work, and there continue to be successful prosecutions of polygamists.