Well Ron, you seem to take the words "public square" quite literally. In fact, you're view of sppech in general is quite narrow and seemingly reserved to oral recitation on a soapbox in a park with pigeons. :-)
But, I'm going to prove to you that a school is the public square.
Students in any public school in America can wear jewlery, t-shirts or any other acceptable clothing advertising their religious convictions. They can pray in the hallway, they can proselytise between class and they can sing hymns under the flag pole if they so desire. All of these are speech Ron and it can be Constitutionally exercised in the public square, ie; schools.
Do you think the state can tell me that I can't wear my crucifx around my neck in federal buildings?
I prefer eagles. But, no, I also think that the press and the airwaves are also part of the public square. When students wear jewelry (such as a crucifix), clothing, etc., denoting their membership in a particular religious community, on their own or their parent's direction, they are expressing their own beliefs in their own way, and one that does not impose or disrupt (despite what any atheist may say). The government is not telling them what type of religion is acceptable or admirable, etc. But when prayers are led by a teacher, or led by a student under the direction of a teacher, then the government is saying, "You should pray, and this is how". That's unacceptable to me, and apparently to the law.
I wouldn't think there's a problem with any of the other activities you mention, except perhaps with proselytizing other students. That last has the potential to be intrusive, depending on the methods, etc., used. Praying in the hallway is O.K. as long as they don't block it, or block access to some kid's locker.