Engineering in Maharashtra

With 96 marks in JEE Mains and having OBC category, it's quite difficult to get into any NIT/IIIT.
However you reside in Maharashtra, so there are fair chances that you will get admission in the govt. /private colleges of Maharashtra. So keep visiting your nearby colleges and gather information.

Firstly, OBC is not a caste, it's a category. Quickly coming to your answer part, yes, you can get admission in Maharashtra colleges with your JEE marks.

College of Engineering, Pune
Narsee Monjee Institute of Management Studies, Mumbai
Sinhgad College of Engineering, Pune
Mukesh Patel School of Technology Management and Engineering
Ajeenkya DY Patil University, Pune
Terna Public Charitable Trust's Terna Engineering College

You have to qualify the LEET entrance exam to pursue engineering from Maharashtra.

If you want to take admission through MHCET then appear for the entrance exam and also that college will also be taking admission on the basis of JEE Mains rank. So, if you want to appear for Mains then appear for the exam.

Yes, you can study the same through MHCET entrance exam.

You can appear for JEE Mains.

You can check the below mentioned link:
https://www.shiksha.com/top-mechanical-engineering-colleges-in-maharashtra-rankingpage-48-0-114-0-0

Ya.after HSC your child can give the CET exam if s/he wants to take admission for any branch in maharashtra.These exams are held every year in the month of April and s/he have to score very good marks in order to get a good college.