Study Abroad

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.

Yes, you can by all means apply. If you have no back logs, have good or reasonable grades then your admission will have normal process. Both countries have best universities and it is just that you will have see what is the best one for you. Both country requires language proficiency test mostly IELTS. You must have 6.5 bands in all four modules and this one of the basic requirements. The university policies may differ from one to the other.

Carnegie Mellon University
Stanford University
Cornell University Of Wisconsin
Columbia University of Maryland
University of Southern California
New York University
Above are some of the universities where you can do MS in data science.

It depends on you, there are good colleges in India namely the IIMs, colleges in Mumbai, Bangalore and so on. Doing your Masters abroad, will need you to get a good IELTS or TOEFL score, which will then help you getting a good university. It depends on you where do you want to see yourself from now, as both the options are good.