IIT

IIT, Bhubaneshwar is better than IIT Dhanbad. I was getting mechanical in IIT Dhanbad but still preferred IIT Bhubaneshwar Civil more.

It's really good. You will enjoy the company of all the faculty members. And when we talk about the infrastructure, it's really awesome. Just visit the campuses once if you had not visited yet. Go for it, dear.
Best of luck.

Andhra University - AU
Banaras Hindu University - BHU
Andhra University
Banaras Hindu University
Berhampur University (BU)
College of Science & Technology - Visakhapatnam, Andhra Pradesh
Dr. Harisingh Gour Mahavidyalaya
IIT Kharagpur
Indian Institute of Information Technology - Allahabad, Uttar Pradesh
Indian Institute of Technology - Kharagpur, West Bengal
Indian Institute of Technology - Mumbai, Maharashtra
Indian Institute of Technology, Roorkee
Indian School of Mines, Dhanbad
Osmania University - Hyderabad, Andhra Pradesh
University of Roorkee.

Comparison wise, IIT will always stand out, and Dhanbad is one of the leading IIT campus.

IIT Bombay, Delhi, Kanpur (almost equal)
IIT Madras
IIT KGP
IIT Guwahati
IIT Hyderabad
IIT Roorkee, ISM Dhanbad, IIT-BHU (and new IITs). .

Here, I mentioning a link:
https://www.google.co.in/url?sa=t&source=web&rct=j&url=http://www.indiaeducation.net/engineering/engineering-branch/list/agricultural-engineering.html&ved=0ahUKEwiO-4qSmPbbAhXGto8KHRQSDJ0QFggmMAA&usg=AOvVaw3izfHa-mP04BTrYG-lYPvc.

You should prefer IIT BHU. It is a better choice.
All the best.

Yes, you can appear in AAT for admission to IIT.

You can compare your rank with the previous year's category wise cut-off's ranks at:
https://josaa.nic.in/josaaorcrarchieve/Result/OpeningClosingRankArchieveN.aspx?Year=2017
There you would get an idea of your selection.