Ok...well I am a student and I have been in the exact same situation with the whole phone ringing in class...except my teacher knew he is NOT suppose to look through any student property; including gym bags and all. In my case my teacher did not go through anyone's belongings but he asks all the students that had cell phones in a specific area in the room to take out their cell phones to check if they were on(we are allowed to have cell phones in school, but they must be turned off during class periods). And in this situation the student has the right to give the teacher their cell phone or not. The only consequence you may recieve as a student would be "being insubordinant"(sorry may be misspelled). Other than this extra info. I have given you, NO... teachers are NOT allowed to look through student belongings. I believe it varies in some work related situations as well.

School officials in public shools have more leniency when it comes to searching personal belongings of students than a police officer would if you were off school property.  Here's some legal info on the topic:

The Fourth Amendment to the U.S. Constitution guarantees "the right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures." Before 1985, doubt existed about whether this right applied to students in the public schools. Schools argued that administrators acted in loco parentis—in the place of the parent—while students were at school. In 1985, the U.S. Supreme Court determined that the Fourth Amendment applies to students in the public schools (New Jersey v. T.L.O., 1985). The Court concluded, however, that the school environment requires an easing of the restriction to which searches by public authorities are normally subject. School officials, therefore, do not need probable cause or a warrant to search students.

The Court articulated a standard for student searches: reasonable suspicion. Reasonable suspicion is satisfied when two conditions exist: (1) the search is justified at its inception, meaning that there are reasonable grounds for suspecting that the search will reveal evidence that the student has violated or is violating the law or school rules, and (2) the search is reasonably related in scope to the circumstances that justified the search, meaning that the measures used to conduct the search are reasonably related to the objectives of the search and that the search is not excessively intrusive in light of the student's age and sex and the nature of the offense.

With regards to searches and minor children in school; Although a school representitive can search a school locker (because it is actually school property on loan to the student). Searching their person or personal belongings such as a backpack while on their person is only legal IF the student allows the act. If the student refuses a search by a school representitive "and each and every student should be instructed to do so" they cannot force a search of a minor...legally. Don't believe the hype you may hear to the contrary they simply cannot do this. So to answer your question; Only if you allow them to.

I would let common sense prevail here. If you have reason to believe the student may have a weapon get the vice principal or other administrator to advise you ASAP. Never search anything without a higher authority with you. In the case of the cell phones ringing, if the student will not voluntarily turn it off have him/her place it somewhere where it can not disturb others (outside, closet, etc.).

yes

That's not legal.

Amusingly, it IS legal for the school to search the lockers!