IIT

then u should go for MBA.good luck.

Yes, you are eligible for MBA.

Yes Allen is the best right now and it's whole system is built so nicely that if you work you will get result.

Since you plan to give CAT after three years ,it would be better to now concentrate on your M.Sc & try and score well. Preparation for CAT doesn't require more than 6 months of sincere effort. CAT exams are normally conducted between Nov & Feb ,so one should start preparing 6 months prior to the date of the open test.
Since you plan to pursue MBA after 3 years it is advisable that you pick up a work assignment & gain valuable experience .This work experience will come to your advantage during the campus placement process at MBA

iit are autonomous colleges
1 year fees earlier was 90,000rs
but the new revised fees applicable in 2016 is 190,000rs
also hostel fees are different in each iits
u can check website of each iit forfee details
but u can expect 3000-6000rs per semester
pls upvote

Check the following link :
https://www.shiksha.com/top-engineering-colleges-in-maharashtra-rankingpage-44-0-114-0-0

Yes you are eligible for admission to M.Sc Maths in any university in India including IITs.

Follow the link for details :
http://www.alljobopening.com/top-iit-jee-coaching-ranking-jabalpur/

That totally depends on your grasping power and how you manage your daily schedule , make a daily plan and focus on your weak areas first , in 10-15 days you will get an exact idea on which subjects you need how much time and the overall time needed