Colleges in Bangalore

If your Bachelors in Pharmacy degree will provide you a lot of knowledge and insight, additional education will give you even more focused knowledge. If you decide to continue your education, you will gain expertise in your subject of study.
You can choose MBA in Pharmaceutical Management. Postgraduate studies always lead to better career prospects. You will most likely start in a managerial position, or even if you don't, you will get promoted faster. Study further to have a great career.

Mathematics, along with physics and chemistry in class 12th, are compulsory for the BSc. course.

Unfortunately, no. The website states, "The candidates must have studied Physics. Chemistry and Mathematics as main subjects in their qualifying exam along with any other subjects. "
However, don't lose hope; there are other research-oriented colleges where you can still apply.

Yes, it is. Physics, Chemistry and mathematics are mandatory to apply for UG programme, even if you apply via NEET.

Unfortunately, no, only 1-year dropper students are allowed. That is, students who have passed 12th in the year of admission or the year before that.

That's not how it works. In IISER Pune and IISc, you can't choose your subject before admission. After two years in IISER Pune and three semesters in IISc, you can select your major subjects. Then you'll have to study the courses specified by the respective department; you can choose astrophysics if you have a course. Also, you can do your thesis in astrophysics if you want.

You can fill up counselling form online and wait to get a seat. With your rank you can also try for RV, PSET, BMSCE college of engineering.

You must have to clear CAT entrance exam with good percentile first.

It depends upon your interest and career building. You've to decide what kind of placement and teaching methods the college have, then you start your career. After all, I recommend some colleges for you in Bangalore those are.
1-Christ University
2-Jain University
3-Bangalore University
4-Reva University
5-BMS management institute.