Indian Institute of Science

It is a 4-year course.

Yes, the admissions were over in April itself.

Hello Jyoti,
It's very tough to say which department of IISc is better than the other. In fact each department competes with another for academic excellence in this institute. I would rather advise you to select the topic that fascinates you the most amongst a variety of subjects that you are eligible. I am attaching a link for you:
https://www.iisc.ac.in/admissions/research-programmes/

The best colleges are
-Indian Institute of Space Physics (Kolkata)
-Raman Research Institute (Bangalore)
-IUCAA (Pune)
Good luck.

You can apply to IISc, if you are appearing in NEET 2018 and securing a minimum of 60% marks (GN), 54% marks (OBC-NCL), 30% marks (SC/ST/PWD). Admission will be based on your rank.

The cut-offs of NEET All India Rank (overall rank)for shortlisted candidates in different categories in the UG stream are:
280 (General),
8000 (OBC-NCL),
8000 (SC),
16000 (ST),
8000 (KM),
and 8000 (PH).

The revision of the date cannot be expected. The classes will be starting in the month of August, so you cannot expect any revision.

Here is some helpful information for you-
http://bio.iisc.ac.in/?q=content/integrated-phd-and-phd-programme.