BITS Pilani - Birla Institute of Technology and Science

Chances are slim due to low academic and CAT score.

Yes, you can apply to the JEE Mains but you won't get admission to NITs or CFTIs based on your JEE Mains. Even your score card will not be released. If you qualify the criteria for JEE Advanced (top 1% and others) based on your Mains exam, you can give the JEE Advanced.
So, for you, the sole purpose of giving JEE Mains will be to get into IITs and not NITs.
You can apply for BITS Pilani too.

You have a low chance of call as you have a moderately low academic score.

No, this institute is an autonomous body and is administered by BIRLA TRUST.

Low percentile. relatively low chances.

Your CAT percentile is a bit on the lower side. You might get a call if you prepare a befitting SOP. Conversion of call depends on your performance in GDPI and your academic score.

GD/Interview will be held from 1st week of March to 4th week of April 2016.
Yes you can reschedule your allotted date by sending a prior notice to the administration.

The faculty are all Doctorates. The faculty student ration is 1:5. Average placement for 2014-16 batch is 8.57lpa and the placement process is still underway.

You CAt percentile is low but you have a good academic record. Prepare a strong SOP and you might get a call.

Yes the placements this year have been better than the last years. The average figure has touched 8.57lpa while the placement process is still underway and this number is expected to increase.