Do German professors in a Master’s program respond to students who email them interested in their research work?
Generally, there is nothing wrong with sending e-mails to professors which demonstrate some interest in their research, also in Germany (where I work). It could help you get in contact with research groups you are interested in. However, it could also happen that you will get no response. 

One reason is that most students starting with a Master´s program will not make contact to the professors, you just enroll and that´s it. During the typically two years of the studies, you will get to know the professors and other people involved in teaching and research. Then, as soon as you have to do some research related thing (some small project or your Master´s thesis), you make contact asking professors or other approriate staff if they would support you with this. Again, trying to make contact earlier probably will not harm, but do not expect too much of it. 

Tours with individual students who are early in their Master´s program are unusual in my experience. But if you show some genuine interest, it might happen. Again: There is no harm in asking! There might also be some organized tours in the beginning of your studies. 

As far as the title is concerned, I would always go for the formal version which is "Prof. Dr." (unisex) in your case. Many people will not even notice if you write "Herr" (for men) or "Frau" (for women) or only "Prof." (unisex), but enough professors will, so it is better to be on the safe side. I recommend to drop the formal part only after some personal contact which justifies it, e.g. if the professor offers you to address them with their first name. 



It would however be strange to use "Herr" or "Frau" in an e-mail which is otherwise written in English. Use them only when you write in German.