JEE

As you are fronm Telangana you can get EEE branch in NIT Warangal. Yet you have second attempt and advance too you can get much more than this all the best.

I don't think reapplication will start for second attempt yet. You can still mail them your issue or contact them by the phone number available on their website in contact us section and test your luck.

Yes, they will accept JEE Mains score.

Yes, for JEE, the minimum percentage required is 50%.

It is both entrance and merit based.

No, it's not important to give both the exams but you should give it for enhancing your score.

You can get non-core branches at this percentile score in special rounds if your state of eligibility is Punjab in the JEE Main exam.

Yes, you can get admissions in non-core branches if you try in csab round of counselling. Moreover, it depends on your state of eligibility.

Yes, as per the criteria, The candidates should have a minimum of 60% marks in aggregate or an equivalent grade in 12th. Moreover, 97.7 is a good percentile score that can get you admission is jiit in CSE and IT branches.

You can take admission in:
Hindu college, Delhi
Loyola college, Chennai
St. Stephens college, Delhi
Christ University, Bengaluru
Hansraj college, Delhi.