How is the First Amendment enforced, that is, which branch of the federal government "interprets" or settles challenges to the document setting the structure and form of the government, and amendments to that document?

Judiciary can struck any laws that prohibits the freedoms mentioned in the First Amendment.

Explanation:

Judiciary enforces the first amendment. The  first amendment prevents the government form making laws that can prohibit freedom of peaceful assembly,speech, religion, press, and religion. The US supreme court can struck down any law passed by the congress that violates any of these freedoms. The first amendment is the part of Bill of Rights, it was ratified on 15th December, 1791.

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