MBA Entrance Exam

Very soon, it depends upon MAT term it will be executed by June and July mostly for the registration and applying for the Exams.
All the best.

Yes, it does. Students writing their final degree examinations during March-May 2017 are also eligible to apply. Minimum score specified for MAT/CAT/CMAT/XAT/ATMA/GMAT is only an eligibility criteria and the actual score thereof shall have no bearing in the selection process.

XAT 2018 registration will open in the month of Aug 2017. The exam is likely to be held in Jan 2018. You are advised to look for XAT notification for exact details and dates in the month of Aug.

It all depends on how comfortable you are with the syllabus. Practice basics for a month in all the areas and then focus on solving mocks.

No, it actually doesn't cover good colleges.
Only limited good colleges accept ATMA.
I will advice you to give CAT, CMAT, MAT, etc.
CAT exam is widely accepted by all the top colleges in India except for those top colleges which have their own entrance exams.
Apart from CAT, there are some other good colleges which have their own entrance exams like XAT, IIFT, SNAP, TISSNET, NMAT, MICAT and IRMA.
Other national or state level exams are:
CMAT, MAT, ATMA and MHCET.
But yes, ATMA and MAT are the easiest exams among all of them.

If you are a fresher then paying this high fee is not a good decision. Your RoI will be poor and you will have a very long period up to few years to break even the cost of education.

The only top college in Pune is Pumba and the percentile cutoff is above 95percenttile. Other colleges which are decent are Indira and MIT but there cut-offs too are above 80percenttile. You may get into Sinhagad. But go for Sinhagad only if you want to go for MBA this year itself otherwise please avoid it and try again next year for some better colleges.

T.I.M.E is the best institute for you.

It is tough to get into MIT and Indira unless you belong to some reserved category. But good chances for DY and Singhad.

It might be low if MIT offers such a course because the main program cutoffs are around 75%tile. So, the ABM course might come around 60 - 65 percentile or even lower.