It's not illegal to bring an animal to school, although it's usually against school rules, unless on certain days that allow you to show your animal or pet.
As long as you have prior approval of bringing the animal or pet to school then it's perfectly legal and okay to do so.
But bringing an animal or pet to school without prior approval from the school, is often against school policy as a result of health, safety and distraction concerns.
Schools, though do however have to make exceptions for students that have disabilities and need a service animal, although the specific procedures may vary by district.
Students that have disabilities and require a service animal, have the right to be accompanied by their service animal, and schools must allow the service animal.
Schools can also legally take your stuff under specific circumstances.
Schools can mainly take your stuff legally under "reasonable suspicion" that you have broken a school rule or law.
The search or confiscation of your stuff has to be justified at it's beginning and conducted in a way that also reasonable given the situation, and not excessively intrusive.
For example if you bring a knife to school or bullets or anything else that is dangerous then the school can legally take the knife or other dangerous items from you and they can and will call the police if the items are dangerous.
Or if you are using your phone in class when you're not supposed to, then the school or teacher can take your phone and hold it until class is over and they usually give it back to you after class.
School officials though cannot simply search you or your belongings without a specific and reasonable belief that the search will turn up any evidence or a violation.
This is a lower standard than the probable cause that is required for police searches outside of school.
The search that the school does on you and your belongings also has to be for the purpose of finding evidences of a rule or a law violation.
For example your teacher may search your backpack if they suspect the student is hiding a weapon or drugs.
The scope of the search also must be proportional to the violation that is suspected.
A search cannot be excessively intrusive and is also judged based on factors like the student's gender and age, and the gender of the staff member doing the search.
A teacher can take and confiscate items that are disruptive like taking your phone that is causing a distraction in class, which is usually for the rest of the class period or until the end of the day.
If a teacher also suspects a student has a weapon, they can search the student's belongings, to look for that weapon.
Some schools also use random metal detectors to search for illegal and dangerous items as well.