B.Sc Chemistry

You should go for M.Sc because you have got a great experience of that field rather than choosing MBA. But you can also choose MBA if you have interest in it.

Yes, you can apply but you must have mathematics as a subject in your 10+2 course.
Thank you.

No, as you said that you are already pursuing, you don't need to give any entrance exam.

No special preparations are required as such. Delhi University does not conduct any exam for B.Sc Chemistry. Class 12th marks are used in for admission in the university.

Tezpur University is really a good university and has earned the recognition from all over the country. To crack TUEE, you just need to get your NCERT basics clear and sorted. After that practise some questions from the previous year papers of Assam CEE and you are good to go. The difficulty level of the paper is not much, it's the limited number of seats that offer massive competition. As for the 2nd part of the question, there is IIT Guwahati and NIT Silchar which can offer you your recommended course but I am not sure whether it is an integrated one or not. Hope this helped!

Yes, you are eligible for this, and if you have any problem, then make an affidavit of a gap certificate. That will be better for you.