The Establishment Clause ensures that government does not favor any particular religion and The Lemon Test was put in place by the Supreme Court to assess laws and ensure that they do not favor or promote religion, and also monitors the governments involvement with religion.
Yes, the burning of the US flag is protected by the First Amendment. This law was the result from the Texas v. Johnson case. In the case, it was deemed that the burning of the US flag was a way for a citizen to express themselves, and this act prohibits the government to punish someone for burning the US flag just because someone or society does not agree with the act.
When someone says “I’m taking the Fifth,” they are exercising their right to not answer questions that could possibly incriminate them.