Science

Yes, you are absolutely right. Nowadays there are so many students pursuing engineering courses, you should surely go for courses other than this to stand out of the crowd. E.g. - hotel management, BBA fashion designing, etc. I am attaching a link for you to have a better idea:
https://www.apnaahangout.com/good-courses-other-than-engineering-after-12th-science/

It depends upon them that how they calculate it. So it'd be better if you ask the college directly. In general, backlogs are counted subject wise. But the plus point is your 3+ year of work experience. You still have the good chance to ensure your selection in your desired college.

Many courses are available brother. B.Sc. Degree in biology/botany/zoology, B.Sc. Microbiology, B.Sc. Biotechnology, computer engineering, B.Sc. Computers, B.Sc. Agriculture, etc.

No, selection of students is based on the marks obtained in 11th and 12th standard.

Please check the following link:
https://www.google.co.in/amp/s/www.shiksha.com/college/national-institute-of-science-education-and-research/exams/amp/nest

Ahmedabad is called the Manchester of india.