Actually, the SCOTUS has ruled the opposite. In the case Tinker vs. Des Moines, the court ruled that the students who were wearing arm-bands as a protest against the Vietnam War enjoyed first-amendment protection and discipline from the school was illegal. The court has been much more lenient on searches -- see New Jersey v T. L. O. However, you still need at least some reasonable ground for a search to be legal.

As for interrogations, the supreme court has yet to rule on it. There is, however, a case brewing: http://www.csmonitor.com/USA/Justice/2010/0405/Supreme-Court.... The fact that it's written in such a fashion as to be assumed that students have Fifth Amendment rights and the court cases are arguing over a technicality of pre-trial processing would seem to imply that students don't shed that right, either. Specifically: "A juvenile court judge determined that Paul did not understand that he had a right to remain silent and a right to have a lawyer and his parents present for the entire interrogation. The judge ruled that police coerced Paul’s confession."