Engineer exams

The government of India is now planning to conduct a single entrance exam for all government and private engineering colleges in India. The JEE Mains exam which is conducted by CBSE for admission may end from the year 2018.
This is similar to NEET which replaced AIPMT.
The final decision will soon be updated.

The Government of India is reconsidering to conduct a Common Entrance Test for admissions engineering collegesacross the country from 2018. A final decision rests on theassessment on the impact of theNational Eligibility cum Entrance Test held on the 7th May, 2017. Some state Governments are not in agreement with the proposal.

Yes, you are eligible but in case of counselling home state candidates are preferred so you should score high marks as you can.

We can't predict whether all the state level entrance exams are going to be one (JEE) or not.
But in 2017, many prestigious institutes in India changed their intake system from state-level exams to JEE.
For example, HBTI used to offer admissions through UPTU but from 2017 admission will be based on JEE Mains. S, it is not going to happen in 2018, but in upcoming years there will be only one exam, JEE.

Sorry to say, but you have missed all the important engineering exams dates of 2017.
So, you should try next year for admission.
I am sad for you. But, you can't do anything.

Yes, you can attend exams like above you mentioned but it is compulsory to get 75% in your 12th board and 65% if ST/SC candidate.

You can appear for JEE Mains and Advanced, ComedK, BITSAT, MHT-CET and UPSEE.

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.