No, they are demanding that the United States government follow the constitution:
The Fourteenth Amendment to the U.S. Constitution guarantees equal protection of the law from state to state, so a legal marriage in one state cannot be denied recognition in another state.
No. They are fighting to have the same rights as heterosexuals.
The ability to fight has nothing to do with sexual orientation.
Gay people are treated better than they used to be in some areas because of the hard work of people fighting for equal rights.
If you are asking if gay rights are of Christian origin, the answer is no. In fact, one of the main reasons gay people are fighting for equality is because of Christianity.
Since the US Constitution says nothing at all about human sexuality, we can infer that gay people have (or should have) the same rights as other citizens.
Initially, the objectives were to decriminalize same-sex relationships. Today, gay and lesbian people are fighting for full equality.
so they can be gay
Some will be of course but the main will be straight. You will find this calculation the same for any concert whether or not the celebrities are straight or gay.
Because they are people and the constitution holds that is self evident that all people are created equal.
Constitution
In the 1970s, the struggle was more basic. Gay people were fighting for the right to not be arrested for their private relationships. They were also fighting for the right not to be beaten up or attacked simply for walking down the street.The fight didn't expand much to other rights such as hospital visitation, marriage, adoption, and military service until the early 2000s.
Yes, they are capable, and have already done so in every war ever fought.