First up, while I live and work in Germany and do have some insights in the "privacy" status quo, I am not a lawyer and can therefore not give you any legal advice. I can only share my personal points of view.
Having said that, let's dive in:
I doubt your teacher presented the browsing history of your home computer. If he/she presented the browsing history of one or more computers at the university/school, that's absolutely OK, since they are property of the university/school. If you look through the legal documentation you've signed, you'll discover that they will have reserved all rights related to the materials and machines they provide. This covers the browsing histories of all their computers too.
I don't see any "gross privacy invasion" there.
Public records are public... which is also true in Germany.
I don't see any "gross privacy invasion" there either.
As for non-public records, the options depend on the kind of party that retrieves the record.
Let's take a university… it's common practice for them to share the non-public information they gain (from the state and/or it's institutions) with the profs who teach you. While such non-public information should (as in "optional") remain confidential, it can (as in "optional") be used under certain circumstances (eg: to represent a practical example) as long as there's nothing negative in your records. If - on the other hand - your criminal records show you have a criminal history, sharing that information is - in most cases - a direct violation to privacy-related laws.
Depending on your own feel, you should clear related doubts by asking a German lawyer. They don't ask too much for a counseling (in German: "Beratungs-Stunde") and they give you a legally secured perspective on what happened and what you can or can not do about it.
You'll need a lawyer if you want to do anything legal in a privacy-violation case, as you really need to be sure your privacy has indeed been invaded. Also, any related legal battle will be long and based on "hard proof" only. This means that you have to collect evidence, signed reports by witnesses, etc. as soon and as many as possible.
In the end, it's up to you what you decide to do. Depending on the details, a lawyer may very well be able to help you. Yet, remember that there's not much money in "damages" to gain here in Germany. So it could be that you sue them for years… only to win a costly "sorry" and a handshake.