No, the laws regarding religious freedom make churches their own judge on what happens inside them as long as it doesn't break the law.
Yes. A church that permits opposite-sex couples to marry, should also permit same-sex couples to marry.
In some jurisdictions, they can legally marry the same as any other couple. In other jurisdictions, it is not legally possible for them to marry.
Massachusetts
As of June 26, 2015, same-sex couples may marry in Ohio.
The state of Connecticut now permits same-sex couples to marry.
The state of Delaware now permits same-sex couples to marry.
The state of Iowa now permits same-sex couples to marry.
New Hampshire now permits same-sex couples to marry.
The City of Washington DC now permits same-sex couples to marry.
Effective June 26, 2015, same-sex couples may marry in any county in Arkansas.
Nowhere. Same-sex marriage is not legal in Trinidad.
Sierra will marry Dylan