It is not illegal for the teacher to go on facebook. If your 10 year old is on facebook and does not want people to see what she posts, unless it is her friends, make sure that her profile is private and ensure that her "friends" are people that she knows and wants to share information with. Also, the school is giving you a heads up about an event/altercation that perhaps you were not aware of or were not aware that it was ongoing -- which is arguably a very good thing for the school to do so that you can help your daughter deal with what is going on. Good luck.
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No, there is nothing illegal about it. There is no legal expectation of privacy in public places (where the fight occurred) and there certainly is no legal expectation of privacy on things posted on Facebook. It is also not against the law to be busy body, and people have broad first amendment protections to speak and act as they choose. If you don't want people in your business, putting it on Facebook is not the way to go.
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My question is why would a 10 year old have a facebook account that is open to the general public? Instead of being concerned about a caring teacher who used offtime to make sure your child is protected, why don't you monitor your child's facebook account or consider removing it altogether?