B.Sc

It depends on your interest. Both the courses are good but B.Sc nursing has large scope. There comes large vacancies for nurses every year because nurses are required in many places like hospitals, schools, healthcare centers, etc.

You have to appear for entrance exam conducted by the university for taking admission in these courses. Basically both the courses are of different:
https://www.google.co.in/amp/s/www.shiksha.com/science/articles/amp/top-10-bsc-msc-colleges-in-india-blogId-13473
For B.Sc course:
https://www.shiksha.com/b-tech/ranking/top-bio-technology-colleges-in-india/54-2-0-0-0

Dear Kareena,
The scope of horticulture is in a good range. Lucrative jobs are District Horticulture Officer, Technical Assistant in CSIR, DRDO, IRAI, Project Manager, Professor, Assistant Manager in HRD, and Scientist. PCMB is mandatory.
All the best for your future.

I would suggest doing B.Sc. As nowadays, IIMs do not prefer B.Tech or BE degree holders.
Even there might be a discrimination against you during the interview due to an engineering background, but it's okay if you want to make your career in the IT field, all you need to do is have some work experience. Else, I would suggest you one more thing, if you are capable of doing your graduation from Germany then you will have a chance to get the job in Germany after graduation. If you want to stay in India go through B.Sc and meanwhile prepare for CAT as well.

No, it is not necessary. You start a new career after 12th class in a new field.

B.Sc Math Honours: Eligibility:
The normal eligibility criteria for B.Sc. Math Honours degree course is a pass degree in 10+2 or equivalent examination in Science stream with at least 50% marks obtained by candidates in Mathematics subject or in aggregate from a recognised board or institute.
Regards.

B.Sc Mathematics is currently not in the curriculum of St. Aloysius College, Bangalore. Please refer to the link provided below for a detailed list of all courses offered by this college.
Regards.
https://www.shiksha.com/college/st-aloysius-college-magaluru-mangalore-49411