Engineering

The final AIR will be declared after April 2019 considering the best score out of the two JEE Main attempts for all the applicants, hence based on current percentile we cannot predict your rank. Wait for the final AIR declaration.
Details:
https://www.shiksha.com/b-tech/articles/how-to-calculate-jee

Over all placement at Parul University is good. What course are you interested in?

List of colleges affiliated to Cochin University of Science and Technology:Cochin University of Science and Technology (CUSAT) is a government owned autonomous university in Kochi (Cochin), Kerala, India. Apart from these there are many government and non-government institutions affiliated with CUSA

Yes, you can get admission in some private colleges and universities. For IIT and NIIT you are not eligible. Some colleges conduct own entrance exam, so try to clear and get some good colleges because at the time of placement, college matters a lot.

Listing some colleges do check the list below:
Sydenham Institute of Management Studies,
Research and Entrepreneurship Education
JBIMS
Durgadevi Saraf Institute of Management
Guru Nanak Institute Of Management Studies
Jankidevi Bajaj Institute of Management Studies (JDBIMS ).

You can directly approach college for free seats, but you'll get a private college.

I believe you must have experienced B.Tech course, which focuses more on technical aspects not on the research/Science aspects. So, rather than taking suggestions from other people you should evaluate yourself on the basis of your experience. And, then decide whether you want to master in the detail

You are eligible for lateral admission. Visit site: http://www.paruluniversity.ac.in/admission/admission-process/admission-procedure/