Noida

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University of Mumbai, Kalina Campus offers Diploma in Hindustani Classical Vocal/ Light Vocal/ Sitar/ Tabla for class 10th pass outs. However, I am not sure about such institutes in Delhi/NCR location.
For more colleges, click below
https://www.shiksha.com/arts-fine-visual-performing/music/colleges/diploma-courses-india.

The Counselors, Navi Mumbai which is affiliated to RKDF University offers MPH via distance mode. It's total Fees is INR 60,000.
Please click below for more details. https://www.shiksha.com/medicine-health-sciences/public-health-management/course/m-sc-in-public-health-science-the-counselors-navi-mumbai-287611.

I'll prefer you to opt for the IIMT, as this is the best college in all the other colleges in your list as this college has best faculty that a private college can have, provides the excellent placements in the whole region and has the top class infra of the college.

Amity is also renowned for its ROI and other good things such as its placements, faculties, infrastructure, and many facilities which they provide to their students. Students themselves feel a drastic change in their personality as Amity conduct so many grooming sessions and mock GD-PI sessions.
Those 4 years would be the best years of your life as you can see many ups and downs where you can learn how to float with the situation.
So, all the best and take a wise decision.

It will cost you around INR 12-14 lakhs for the whole course including standard hostel rent and mess charges.

No I'll prefer you to opt for the amity as this is the best college as this is the best college in terms of faculty, infra and also in the placements.

See, if you are joing a college as per the area then I would suggest you to opt for Solan as this is the best college for the same and the most important thing is that Shimla is very near to that college but if you are going for the placements then opt for Noida campus.

I would suggest you opt for Manipal Sikkim as this is a better college in all terms.