Germany

Technical University of Munich
RWTH Aachen University
Karlsruhe Institute of Technology
Technical University of Berlin
TU Darmstadt
University of Stuttgart
TU Chemnitz
TU Clausthal
BTU Cottbus-Senftenberg/Cottbus
These are some of the best universities in Germany to do MS in mechanical engineering.

Opportunities are enormous in Germany. Just don't expect permanent citizenship there so very easily.

Management courses throughout the world have earned the fame. In every country there will be ranges of universities from top to lower classes. It all comes under this point that where you want to do and how much you can afford.

Yes, you can apply with these grades. Make sure you get 6.5 band in all four modules in IELTS.

If that is what you want to do then you should know how good or bad and how beneficial it is for you. It might fetch you a job but clearly it is your decision to make whether to study or not keeping in mind what you expect out of it.

http://hpathy.com/past-present/the-educational-system-of-homeopathy-in-germany/
Refer the above given link.

You cannot directly contact professors unless you have a record of studying in the university in Germany. You may contact the university itself and get more information.

You can choose to be an academic lecturer in a dental college or more options are open after MS. So you can even consider going for Masters.

Physiotherapy isn't a university education in Germany, but a special school. You can learn that at so-called Fachschulen, which isn't free - what I could find is that it's something between 300 euros to 450 euros per month.

There are best colleges in Germany in many fields like management, science, arts, etc. Germany is the most sought country to study when it comes to engineering. Here are some of the best universities to study in:
Universities in Berlin - Free University of Berlin, Humbolt University of Berlin
Universities in Munich - Technical University Munich, Ludwig Maximilian University of Munich
Universities in Smaller German Cities - Heidelberg University, Schiller International University,
Hochschule Furtwangen University, University of Freiburg, Leuphana University Lneburg.