B.Sc Eligibility

Yes, you should be able to pursue B.Sc in radiotherapy after your Diploma provided you meet the minimum requirements to gain admission in B.Sc.
B.Sc Radiotherapy eligibility:
1) 10+2 (Medical) or equivalent with 55% marks.
2) Few institutes conduct entrance exam for admission.

Hello Bhavik,
Of course yes. For admission to B Sc courses, at least till now, there is no entrance exam. It depends on your marks obtained in 12th. So go ahead. Best wishes

Eligibility for B.Sc courses are as follows:
1) Students with 50% in HSC examinations from a recognized education board with science stream can opt for a course in B.Sc.
2) Normally, 50% marks are required at HSC level, however this percentage may vary from state to state or from institute to institute. Few colleges also conduct entrance exams as well.

If you want to become a scientist at ISRO, you should appear for the ISRO qualifying exam rather than appear for GATE.
The eligibility:
BE/B.Tech or equivalent qualification in first class with an aggregate minimum of 65% marks or CGPA 6.84/10 (average of all semesters for which results are available). Minimum of 65% marks or CGPA 6.84 in section B alone for candidates with AMIE/Grad IETE qualification.
The qualification prescribed and the benchmark are only the minimum requirement and fulfilling the same does not automatically make candidates eligible for written test.
To answer your question, GATE syllabus for both would be the same.

You will have to check with the institute which offer admission in MPH, as different institutes have different eligibility criteria for admission into their MPH courses. Please refer to the link provided below for a list of colleges which offer admission into MPH, and their eligibility criterias:
https://www.shiksha.com/medicine-health-sciences/colleges/mph-colleges-india