Exam

It's hard to get admission in JK Institute of Applied Physics with such a rank. CSE branch closes at around 7000.

Hello, Sardar Patel College of Engineering is a government institute. Approximate cut off for:
General-170
OBC-150
SC-70
So it will be tough for you to get this college with your JEE score.

Yes, you are eligible for JEE Mains provided you have 75% in class 12th. It doesn't matter that you have appeared for any other examination or not.

Chandigarh College of Architecture is a prestigious college and there are only a couple of seats there for outside quota.
You have to score something above 265 to secure a seat there through JEE B.Arch paper. This may not be possible for you to take admission in this college.

Follow the following links:
https://www.shiksha.com/b-tech/course/b-tech-in-civil-engineering-national-institute-of-technology-surathkal-Bangalore-61474
https://www.shiksha.com/b-tech/course/b-tech-in-mechanical-engineering-national-institute-of-technology-surathkal-Bangalore-61468
https://www.shiksha.

Admission into MBA without CAT/open test will not lead you to a good college and also will not be of much utility from career perspective.

Hello,
You are eligible for:
Azad Engineering College, Lucknow
Dr. Ram Manohar Lohia Avadh University, Faizabad
Shri Ram Murti Smarak College of Engineering and Technology, Lucknow
These are the few colleges in which you can take admission through your rank (9000) in UPSEE.

No, don't drop a year just for JEE Mains. Drop only if you are targeting JEE Advance and if you want IITs. Still if you are confident enough that you can do very well in JEE Mains next year and are sure to get top NITs, then only drop the year otherwise it's a waste of time.

Yes, you can. Please refer the institute website for further details:
http://www.welingkar.org/pgdm/pdf/Admission_document_PGDM_2018_notification_for_website_PM.pdf

For seeking admission into top 20 MBA colleges one should try and score more than 90 percentile.