IIM Ahmedabad - Indian Institute of Management

I think you need to clear the interview stage cut-off for IIM A to get a call and do well in the interview to convert the interview call. It is not a question of how you completed your degree, but how your composite score (as calculated by IIM A; the process is given on the website) compares with others and whether it makes the cut or not. In the interview, it is likely that this question regarding the completion of your degree would come up, but it is a matter of how well you handle the situation that determines your chances.

It is your prerogative where you want to take a loan from. Each bank has its own application form for the same, but generally, you have to mention the bearer's name for taking any loan.

Both are equally good. You can opt for either of them according to your interest. Just ensure to give your best in them because IIM A prefers students with good academic records.

Sorry to inform you this but your BE score will definitely play a spoil sport for admission to IIM A, no matter how high you score in CAT percentile terms. Having said that, I would suggest you to prepare one more year meticulously, to aim for FMS which does not consider previous academics while selecting candidates for admission.

It is not something one can answer for you. It's something you need to discover for yourself. Rule of thumb: If you want to stick with the technical line then M.Tech. If you are more interested in management then MBA. Refer to this TOI article to make a more informed decision:
http://timesofindia.indiatimes.com/home/education/news/MBA-vs-MTech/articleshow/21908011.cms

No MBA in mergers and acquisitions is not offered by IIM Ahmedabad. IIM A only offers degree in general management. Having said that, you can always take electives regarding mergers and acquisition in 2nd year, if you have particular interest in the said topic.

Yes, its worth every penny. The level of faculty, interaction with peer group and learning is unparalleled in India. Hence, its worth it.
Do understand that unlike other government institutes (read IITs/NITs), IIM's do not take any form of monetary support from government. Hence, the complete expense of the education is born by the students itself rather than the tax-payers of India.

You can start preparing diligently for CAT. If you do not have much idea about CAT, I would suggest you to join a coaching institute with good faculty to help you get the basics right in DILR/Verbal/Quant. After the basics the next challenge is to solve the said question within a stipulated time. Hence, second stage of your preparation should deal with giving mocks and analyzing your mistake repeatedly till CAT.

Sorry to say but your prior academic performance makes it very difficult for you to get a call from IIM A. Having said that, do search for colleges which do not give weightage to previous academics.

There is no hard and fast rule and usually depends on the overall performance of applicant and selection criteria of IIM A of that admission year. As a rule of thumb, 90%+ in 10th/12th and 85% in graduation (read engineering) would require upwards of 99.6 percentile in CAT. The lower the academics, the more the CAT score to compensate. Academic diversity do allow some slack in CAT percentile.