Bachelors

You can consider following colleges:
International School of Aesthetic and spa
VLCC Institute
Rashtrasant Tukadoji Maharaj Nagpur University

Yes, B.Sc in radiology is an undergraduate course but it is not introduced in some of the colleges, so you have to check out for the colleges on Google and all the best for admissions.

There is no problem, if you switch from one board to the another the only thing that depends upon is the quality of education that you get if you are studying in ICSE school and you are getting a poor quality of education then you are the wrong place so the thing that only depends upon is the quality of education, so look forward for the best school and get admission in it.

Yes, graduation in any field can be accepted. Even Students with 3-year graduation and commerce graduate can also apply. But for placements, 1st preference is given to agricultural graduate students.