Engineering Entrance Exam

Yes, you can but the counselling is over so the chance is only available through management quota.

You cannot get a good college on the basis of your JEE score. You can either go for a private college or you can also prepare for JEE and attempt it next year.

BITS Pilani has its own entrance exam, and it is similar for VIT, Thapar University and Bharati Vidyapeeth Pune more or less if you want to pursue B.Tech you have to give an entrance exam, either JEE Mains or any other.

It will depend on the college or your preferred engineering branch.

Your AIR will give better idea of college than marks. According to this year cutoff, 136 is really good marks and you can get state level college with nice branch. Getting a seat in good NIT's is a bit difficult if you belong to general category.
Cut off of JEE Advance is going to be a bit high because maximum marks were high for general category people.

Yes definitely, NCERT has one of the best syllabuses for JEE preparation. You can choose another help book for more knowledge but NCERT is the best for that.

Syllabus of IIT preparation is too long, refer the following link:
http://www.iitjee.org/iit-jee-syllabus.html

Your JEE score is good enough. But your 12th percentage is not enough to make you eligible to get into NIT.

Based on your JEE marks and class 12th percentage you can get a seat in a good NIT and based on your COMEDK rank you can opt for mechanical or civil branch in good colleges and if you are planning for CS, EEE or ECE you can try for colleges like RNSIT, Dayanand Sagar College or Dr. Ambedkar Institute of Technology.

Hi,
Please specify the name of the college in which you want to get admission. As you are trying to mention a college, there are many factors that determine the admission.
With this rank in JEE Mains you cannot get the top NITs.