Anna University

Yes, Anna University-Chennai takes admission on the basis of board score.You can join TNEA counselling for the admission in Anna University. Currently, Anna University is at 8th rank among the engineering institutes in India.

No, you cannot get admission with this score unless your cut off is 190 or above.
Admission into Anna University and its affiliated colleges depends on your caste and their off marks. Calculate your cut off marks and mention your caste then I may help you.
To calculate cut off marks:
1) Maths score divided by 2.
2) Add physics and chemistry marks and then divide it by 4.
3) Add both these marks and you will get a score out of 200.
If that is above 190 you might have chances. Mention your caste also.

For information regarding deduction of fee I would request you to contact the college under Anna University where you wish to apply.
The fee concession is Rs. 2,000 for Government colleges, Rs. 4,000 for Government-aided colleges, and Rs. 20,000 for self-financing colleges, a year. Only students who are admitted through the single window counselling of the Anna University are eligible for this concession.

It would great if you could mention which college do you wish to apply for.

The admission into Anna University and its affiliated colleges is based on your class 12th board exam marks (cut-off marks: the aggregate of maths, physics and chemistry).
You should apply for counselling under Anna University at www.annauniv.edu on or before May 31st and the last date for submission is June 3rd.
As Anna university is a government college, the fee structure will be low. It will be around 40000-50000 per annum.
All the best.

Yes, students from other states of India can also apply for Anna University.
They are admitted through other state quota. The applications for other state quota will be available on the website www.annauniv.edu. The date is not known.
So, you are advised to refer to the link for further details or you can call the admissions office.
All the best.