but, a prayer is is related to (or in other words in respect to) a religion, what they are doing cannot possibly be legal because for it to be legal there would have to be a law about it, and congress is the only body of the government that can write laws, and if it had written a law about this then that would have been a law respecting an establishment of religion, which is specifically not allowed by the first amendment.
...no.
I read legislation for a living, so maybe I have a better grasp on how the wording actually functions, but I'll try to break it down. Here's the relevant part of the First Amendment, for reference:
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof
Congress - Refers to both the House of Representatives and the Senate.
shall make no law - Shall / must are often legally interchanged. This clause prohibits Congress from enacting a law that does
something.
respecting - The
something. Respecting can be interpreted as concerning, enacting, codifying, or otherwise
to do with.
an establishment of religion - Does not necessarily mean making a religion (although it can include it), but rather is referring to religion as an establishment, or a thing itself. So, Congress cannot establish laws concerning the creation of an official religion, nor which are derived from a particular form of religious practice. It does not prevent the exercise of religion by persons, but actually protects it:
or prohibiting the free exercise thereof - Means what it says. Congress cannot prevent a person from freely exercising their religion, whatever it may be.
Law generally works through prohibitions rather than positive requirements. To say a prayer in a state or federal establishment, one does not require a law that says you can. Rather, to be prevented from doing it you require a law that says you cannot.
Nuke pretty much got it correct is his response. And, as I understand the prayer under discussion is not a legal part of official procedure but is a matter of policy or tradition (which I'm guessing is non-binding upon its members) it wouldn't be prohibited under the Constitution.
The only way the First Amendment enters into this case in the context of the State is if they had a formal, binding law that requires all members to participate in a religious prayer within the context of their official duties.
EDIT: The legal separation between religion and state is actually very poorly codified in the United States. Other countries (my own included) have left a much broader definition (2. Everyone has the following fundamental freedoms: (a) freedom of conscience and religion;) which allow the courts significantly more leeway in their interpretations and actually increases the strength of that law. The First Amendment actually handicaps itself by being too specific.