Engineer exams

This is under plan in line with NEET exam however few states have opposed it. Education being a central and state subject, states do not wish to give away the rights considering many engineering institutes owned by politicians ans their relatives ao the matter is in hold as of now.

If you have already taken admission in B.Tech then do not worry about any the entrance test like JEE.
Now, keep studying and prepare for the GATE exam.

No, two year drop is not good. To prepare for entrance exams, one year should be enough. Also, it depends on your ability to crack any exam.

Yes, you can apply for one more entrance exam for engineering, and if you want to pursue B.Tech from Mumbai, then you have to qualifying MHCET entrance exam for same.

Hello,
If you want to know the list of engineering entrance exam for this year, then it is waste as almost all exams are over.
But, if you wants to know entrance exam for next year then from next year. Maybe, there is one single exam just like NEET for getting admission in various engineering college of India.

Please follow this link for complete details of rank and college:
https://www.shiksha.com/b-tech/resources/wbjee-college-predictor

If you want to join any coaching then go for Allen, Resonance, Bansal Classes, etc.
If not then focus on NCERT first solve NCERT first then solve RD Sharma for maths, HC Verma for physics and NCERT is enough for chemistry.
Then solve question banks and previous year questions also.

Check the below exam calendar for the upcoming exams and dates to apply. Register for the same-
https://www.shiksha.com/engineering/resources/exam-calendar