Engineering

No, it is not possible to join Diploma through distance directly in second year. You can join regular Diploma in 2nd year, not the distance one.

Admission is through Tamil Nadu Engineering Admissions (TNEA) counselling based on the marks obtained in 10+2 and with 98% marks, you can surely get petroleum engineering in Alagappa College of Technology (Anna University).

BHU UET is kind of a national entrance exam, as it is conducted in 20 cities across India. For more details, check out the link below :
https://www.shiksha.com/university/banaras-hindu-university/exams/bhu-uet.

TANCET 2018 Application Form is expected to release soon. Candidates can apply for TANCET at its official website i.e. annauniv. Edu. Possession of a Bachelor’s degree is necessary for Tamil Nadu Common Entrance Test.

Yes, you join directly in 2nd year in B.Sc, after completing Diploma in information technology. Check out the links below for details:
https://www.shiksha.com/science/course/b-sc-in-information-technology-lateral-entry-directorate-of-distance-education-Punjab-technical-university-Punjab-other-283877

You need to prepare your statement of purpose, which is actually a 1000 word essay, which you need to mention about the reason of taking this particular course and you need to prepare for the exams assigned at the same time.

Check out the link below for details:
https://www.shiksha.com/engineering/exams/tancet/dates.

Of course, you can either get in through Anna University/TNEA Counseling or contact College for the Management Quota. I am another state student studying in PSG
Check out the link below for details :
https://www.shiksha.com/b-tech/course/b-tech-in-information-technology-psg-college-of-technology-coi