College of Engineering, Anna University

Hey there Akshay!
Well, according to my knowledge, the college is easy even for NRI. This college surely must be irrespective of caste. You may take admission there however you might have to face difficulties regarding conversating with other out there while living in Guindy. I would recommend follow your parents, teachers advises and surely follow your dreams.
Best Wishes.

Well, for 2018, the eligibility score in B.Tech from biotechnology for GATE exam is 38.9 for general category, 35.0 for OBC category and 25.9 for SC/ST/PwD candidates. On the other hand, for TANCET there are different eligibilities for different courses if you are going to opt after B.Tech. For example, if you want to give TANCET to qualify for M.Tech in biotechnology, then the eligibility criteria is to pass in Bachelors degree with atleast 50% and 45% in case of reserved categories. Also, people except from professional institutions are eligible for TANCET in their final year or last semester.

Hello Sir,
Admissions in Tamil Nadu are given fundamentally to the students who are native of Tamilnadu or to some other students meeting the criteria. But from what you have written I do not think that your son is meeting this criteria and hence your son's dream of studying in this college appears to be headed nowhere. However to help you I am attaching link that will give you in detail the eligibility conditions for getting admissions in Tamil Nadu.
https://www.shiksha.com/university/anna-university/tnea-exam
Best wishes.

Yes, you can. There are some universities offering M.Sc. Geology to those students who did not have Geology at B.Sc. level.
Banglore university.

No, you need 190 and above cutoff. This course is core of mechanical and filled with management things.