Mechanical Engineering

Hello Manish, there are 2-3 entrance tests that you ought to give to secure admission in India. One of them is JEE Mains, then JEE Advance. The fees of any engineering college or university is not more than the figures you described. As far as good colleges for Mechanical Engineering are concerned, the link below has the list of them-
https://www.shiksha.com/b-tech/ranking/top-mechanical-engineering-colleges-in-india/48-2-0-0-0

Nowadays, this field is more popular, as Big companies like Wipro, Infosys, IBM, CISCO, Google, and Microsoft are in immense demand for great IT worker. From my view, opt B.Tech CSE, and pursue any other course like ASP.NET, ANDROID.
These are short term courses, which will help you to get easy placements in bigger company with higher package.

No, you can't get mechanical in stream 2. Try for other departments.

You should opt for B.Tech in IT which will provide a handful experience in that field.

Of course Germany, because Engineering is one of the hit courses in Germany. High quality of education with low education costs are one of the biggest lures for students to go to Germany.

You must specify your category, and the exam you gave. If it is JEE, and you fall under general category, then yes, you will easily get some pursue. And, even for other category, with that rank you would get mechanical.

Kindly use the college predictor app. I hope this will resolve your query.
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor
All the best.