Colleges in Delhi

Well, when it comes to DSM, it has got a brand name big enough that a recruiter pays an eye to your profile. Secondly, the location is a major advantage. Located in Delhi, you have many startups based out of NCR visiting the campus. You have the flexibility to go for an off-campus as well.
The campus is very dynamic and you have various events /conclave/seminar happening all throughout the year. The infrastructure is again very new. And you have an excellent team of faculty members to guide you.

The last date for filling application for July 2018 session is 30th June 2018.

No, JIPMER does not accept NEET score. JIPMER has its own entrance exam.

For Hospital and Healthcare top B-Schools are:
Goa Institute of Management-Goa
D.Y. Patil University-Navi Mumbai
Jamia Hamdard University-Delhi
Lovely Professional University-Punjab
Tata Institute of Social Sciences-Mumbai

Your PG marks will carry higher weightage than UG marks. But remember also that the universities consider many other factors also like your recommendation letters, statement of purpose, extra curricular activities and your GMAT score.

I don't think so that the college will allow you to take admission in the final year. However, I would suggest you contact the college officials for more clarity.
Admission is possible only if you get a NOC from your current university.