Exam

For Jamia, if you are looking for a technical course like architecture or engineering, then you have to give JEE in Jamia.

Go to the following webpage and find out all the details of admission to IGRUA. http://igrua.gov.in/How to Apply.htm
For study material, refer any normal NDA entrance book. They usually test your aptitude for this exam.

No, YMCA University takes admissions only by shortlisting students on the basis of their rank in the JEE exam. If you haven't given JEE exam then you aren't qualified to even apply for this university as in the application form itself they will ask you about your marks and rank in the exam and faili

PSG does not accept any JEE ranking. Admission to PSG college is only through single window counseling by Anna University Chennai. This counselling will be based on ranking that is provided to you on the basis of marks obtained in Physics, Chemistry and Mathematics in 12th standard examination held

Yes, if you take a drop this year then you can give both your improvement exam as well as JEE exam again the next year. Since this year, you have qualified for the advance but you can't give it because you don't have 75% in boards. I would personally recommend you to take a drop as this board percen

IMT Nagpur is better than XIME, Kochi in terms of placement, ROI. Location wise Both are same. XIME, Kochi has small batch size in compare to XIME, Kochi.

Your marks are in the top level of safe zone considering your caste. You can easily get the top of the colleges you wish for. You just need to keep an eye on the college and start shortlisting your preference so that it does't create any tension in the end.

Your CAT Percentule is low.
You can try again CAT exam or try another college.
Your academics is also not much attractive.

Depends on several factors:
Your background, academics, interview performance and how you present yourself. Also, depends on your body language as well as tone of your voice.