Exam

Usually, it's not your composite score that is looked at, it's your percentile which gets considered. So, look at your percentile and respective cut-offs.

To know if you can get a call from IIMs or not, you can refer to the below link:
https://www.shiksha.com/mba/resources/iim-call-predictor

Of course, yes. For getting admission in SPA, you have to appear in JEE Mains Paper 2 which is meant for architecture and planning.

Hello,
Yes, you can appear for any national level entrance exam in your final year.
Generally, to get into a college, these exams have post process like GDs and PIs.

Hi,
Colleges do have management quota, wherein, the fee structure is double to triple of the normal fee. You can check with the college in which you are interested.

Hi,
You can check the colleges below:
Jaipuria - Delhi
Amity - Noida
ITM - Navi Mumbai
UBS - Mumbai

Hi,
You might get admission with this score. Do check with the college once for the updated cut-off.

Hi,
1. For Quant, "Quantum CAT" by Arihant Publications.
2. For Grammar: Wren and Martin
3. To work on Vocabulary Word Power made easy Norman Lewis
4. The Most important: Past Years' CAT questions by G.K. Publications
https://www.shiksha.com/mba/articles/important-books-for-cat-2015-preparation-blogId-11