B.Sc Chemistry

B.Sc in Chemistry would be best, if you want to go for Lectureship. You can also go for lectureship through Biochemistry, if you want. There is no foundation on restriction on the career choice after B.Sc. Both will be good for lectureship and biochemistry.

B.Sc. Lateral entry is only possible if you had Diploma in the related field. Also distance for B.Sc. Chemistry is not available everywhere and might not even be valid even if it available. Check this institute. But it also has 3 year course. http://www.imtsedu.com/bsc-chemistry-distance-education.html.

As the college has not disclosed the fee. I request you to contact the college officials on the contact numbers mentioned in the link:
http://www.mountcarmelcollegeblr.co.in/

Eligibility
Candidate must have passed 10+2 from a recognized board.
A similar like was posted sometime ago, please refer to the link below. The answer might be what you are looking for . For precise details, please download college brochure.
https://ask.shiksha.com/what-is-the-eligibility-criteria-to-get-admission-in-loyola-college-for-b-sc-in-chemistry-qna-4314394

If you're focusing on government jobs then physics, geography and maths will be best for you. If you want to go in technical line or banking jobs then computer application will more beneficial. PCM is also a good option for Master's or B.Ed. All the best.

Yes, you are eligible for NIMCET because you passed with a good percentage.

The decision should be based on your interest areas, personality traits and long term career objective. An MBA specialisation can be done in a host of areas and each area has a separate career path and success in it depends a lot on your skills and personality traits. So please introspect & then take the plunge. A person has higher chances of success if he/she pursues a career in his area of interest & passion.

BHU does not offer B.Sc Hons. in chemistry. It only offers B.Sc for maths and bio group. You can check for some other colleges at shiksha.com.