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B.Tech CS is a better option to pursue as it has better career opportunities in future and good jobs.

The 1st year of engineering is common for all, although you are divided into two categories only on the basis of physics group or chemistry group, it depend on the institute.

Your percentile is really low, but still you can get information about ranks and colleges from this link. Hope you will get what you're looking for.
https://www.shiksha.com/college-predictor

Yes, you can now register for CS, and there are 8 subjects in executive stage.

Hi,
Of course you can study M.Sc in computer Science. A lot many students do pursue this course. You have to give TOEFL/IELTS exam and prepare a very good cv/resume for the top universities like Oxford, Cambridge, Princeton etc. Other universities may take admission thorough an entrance exam. Here is a link that will help you:
https://studyabroad.shiksha.com

Yes, Alliance University is a good university for B.Tech in computer science and engineering. there you will be getting a lot of opportunities, exposure and knowledge. The one thing that you have to maintain is your score.

Use this tool to list all colleges you can get. https://www.shiksha.com/college-predictor.

To get admission in a good university in the US, you should have a good score in TOEFL and your Bachelor's degree without any backlogs or supplementary exams.

Please use the college predictor tool by Shiksha. This will help you to predict the college according to your rank/percentile:
https://www.shiksha.com/college-predictor

Yes, according to me, you should go for IIIT and not for IIT as CS has more scope than mechanical and the college doesn't matter in comparison to branch, what will be the benefit if you get a job in mechanical and not get promotion due to its very less scope.