Mechanical Engineering

No, you may have to take WBJEE for that and you will get a seat only if there are seats available. There is no other way.

Kindly visit the link mentioned below:
https://www.shiksha.com/engineering/course/training-diploma-in-mechanical-engineering-international-institute-of-management-and-technical-studies-kolkata-salt-lake-city-257866

College of Engineering, Pune is an autonomous engineering college affiliated to Savitribai Phule Pune University in Pune, Maharashtra, India. Established in 1854, it is one of the oldest engineering colleges in Asia, after IIT-Roorkee. As per my knowledge, the minimum percentage required in last year of Diploma to get admission in COEP is 60%. For more information, you can contact at given below address. Address: Wellesley Rd, Shivajinagar, Pune, Maharashtra 411005
Phone: 020 2550 7000.

Yes, of course, you are eligible.

Yes, you can take admission. To take admission in VJTI for Diploma in mechanical engineering, one should score above 90% (open category).
Hope this will help you.

Major difference is when you graduate from B.Sc. Physics, you will not placed, whereas when you graduate in mechanical, you will definitely get placed somewhere.

You can get more information about it here
https://www.shiksha.com/b-tech/course/b-tech-lateral-entry-college-of-engineering-Pune-shivaji-Nagar-204728.

It depends on your marks in the 1st year because only a limited seats are vacant in that branch. So, the student with higher marks will get the preference. So, if your among the toppers of your college, then you should approach your registrar or the dean of students.

You can proceed with doing B.Tech from a recognized university that helps you more in the field of vehicles. And you were going to get good placement with good salaries and a bright future, as you said that your interested in the field of motors.

Yes, with 71%, you can take admission.