Germany

Yes, and besides you also need to learn German language.

Dear Mohit, you can consider Queen Mary, Cranfield and
Glasgow Caledonian University in UK. In Germany RWTH Aachen University is the best option you can consider. There is another degree offered jointly De Montfort University,Leicester in collaboration with the Faculty of Mathematics
and Engineering at the Fachhochschule Bielefeld (University of Applied Sciences) in Germany. Check all the website for complete information. This programme is an advanced modular programmefor graduates of mechanical and electrical engineering, includes a research project and financial aid too.
Best Wishes

Lateral entry in engineering will not create any problems for admission in German Universities for MS provided your degree is from a recognized university in India.

Dear Nilesh, Germany is a better option for all good reasons. I am not aware of Estonia universities as Germany is more popular. Work permit and PR options are open to international students. If you want to settle down, irrespective of the county you must be qualified and skilled.
Best wishes

No, they are not compulsory but having either one of the scores is an advantage no doubt.

Hi, you can take a look the page here which contains all details https://studyabroad.shiksha.com/germany
Hope it helped.

What course in specific are you looking for? Generally, GMAT/GRE and TOEFL/ IELTS is required for PG. You will also need a resume and LOR from your college professors or employers. They may also require work experience in case of MBA.

MBA in Germany in Automobile Study is best with great opportunity and salaries offered by premium auto companies like Bmw, Merc, Audi which have huge manufacturer base in Germany.

Taking into account US shall cost you around 70-80 Lacs minimum, whereas Germany and UK around 40-60 Lacs. Although, it totally depends and varies from college to college and their rankings.