Diploma

No. Diploma in IT is a 3 years after 10th and 2 years after 12th or ITI.

First of all, you have to take admission in B.Tech through lateral entry. After that, you have to clear GATE with good score after B.Tech after that, you can get M.Tech in IIT through GATE.

You can get top college Maharashtra. First, you should have to collect details of colleges which are giving lateral entry. Then, study the admission procedure and apply for that college.

Yes, you can pursue through lateral entry.

B.Tech will be the best option. From B.Tech, your graduation will be completed and you can also able to give GATE. JE job is also good but it is difficult to quantify because there is very less vacancy nowadays in the government sector.

First you must have successfully completed 3 year Diploma in engineering. Different institutes consider different entrance exams. Most of the regional, government and private colleges take admission on the basis of State entrance exams.
Entrance exams are:-
Calicut University lateral entry entrance exams.
Delhi Technical University lateral entry entrance exam.
KIIT University lateral exams.
LPU NEST.
UKSEE BTech lateral entry entrance exam.

Since you are doing B.Sc through lateral entry system, surely you can take admission in M.Sc in IT by lateral entry system. That would not need the problem. I advise you to just check the colleges like University of Mumbai for this admission. It's a very good college for computer science.

Yes, you are eligible to join.