Engineering in Mumbai

No, it's not necessary to appear in JEE Mains for getting admission in Bachelors in automobile engineering in Amity.
But JEE Mains is one of the way to get admission in this college according to marks obtained in JEE Mains.

IIT Powai is the best Institute for Chemical engineering in Mumbai based on ranking by various rating agencies.

Hello Sadanand, There are very few colleges offering Diploma in mechatronics engineering in Pune and Mumbai. Colleges in Mumbai offering Diploma in Mechatronics :- 1) NMIMS University's Mukesh Patel School of Technology Management and Engineering, 2) Terna Engineering College (TEC, Navi Mumbai), Navi Mumbai

You have completed your Diploma. So, for engineering, go through colleges like VJTI, SP College, Vidyalankar Institute of Technology, Thadomal Shahani Engineering College. These are very prestigious colleges in Mumbai.

Greetings from Shiksha.
You have some chance to get admission in Diploma Mechanical Engineering at Sardar Patel College of Engineering in Mumbai. It is good Institute.

Hello,
Find out your rank with help of any rank calculator online and enter your rank in the link given below and get the list of best colleges by filtering branch as electrical engineering:
https://www.shiksha.com/b-tech/resources/mhcet-college-predictor
Hope this helps All the Best!

Kindly use the college predictor app. I hope this will resolve your query. https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor
All the best.

Sorry to say but you haven't cleared JEE Mains required cutoff. So, there is no way to get the best college for mechanical. You may get admission in any private college on the basis of 12th percentage.