Science

No, you can not do the B.Sc. Nursing course. The eligibility criteria of B.Sc. Nursing is 10+2 class passed with Science (PCB) & English Core/English Elective with aggregate of 45% marks from recognised board under AISSCE/ CBSE/ ICSE/ SSCE/ HSCE or other equivalent Board.

Your 12th marks are very good for getting admission in some reputed private engineering colleges in B.Tech courses. On the basis of your 12th marks you can also get some scholarship. But before come to any conclusion please focus on July JEE Main exam for improvement in previous score.

Education does not have any age, until and unless you want to join the force where there is age cut off.

It is not necessary to take biology in class 12th as the major subjects required for food technology are PCM (PHYSICS, chemistry, maths), but taking biology would be helpful as this course is about food which directly relates to biology because human system, metabolism, nutrition, food microbiology and other aspects of biology are involved.

You can explore the website of Andhra University for the same. Please follow the mentioned link for the Andhra University website. https://www.andhrauniversity.edu.in/academics/courses-offered
If you can't find the previous year's papers there, you can call at helpline number of the University.

Yes, you are eligible. You can pursue your Diploma in food and nutrition.