CAT

BIMTECH Noida, IBS (Hyderabad), IMT (Nagpur), Christ University are some of the institutes you can go to.

Cutoffs is around 80 percentile so you may not be able to get a call from IFMR. But still if you have exceptional profile then you may be able to get a call. They give decent weightage to profile of a candidate. If you have won any national level competition, participated in international level competition and are actively engaged in volunteering then it would be possible to get a call from IFMR. Rest depends on how well you perform in GD-PI.

Yes, you can. There are some seats for non-engineers in IIT-D and some other IIts as well. You can go through the admission criteria of all these institutes and apply for the same.

For CAT, regular practice is the key. There are numerous coaching institute (time, ims, MBA guru, etc.). All of these have decent study material of their own.You can purchase test series of time and ims. From my experience of CAT, this year IMS test series is the best. Practice mock once in every week and analyze them thoroughly. Work on your weak areas.do this repeatedly. CAT is more of a mind game than of skills and knowledge, remember that.

Do you have any significant extra curricular activities?

You can write directly to IIM-Lucknow on their Id or can contact them, but I will advise you to not to take any illegal action because it will ultimately harm you because IIM is a big autonomous body, you shouldn't do any offensive thing against them.

This is a very low score, it will be very difficult to get into good B-School of Bangalore. You can apply through scores of other entrance exams. Generally, colleges look for entrance exam scores as well as academic profile and work profile (if any) to shortlist the students. You have a decent academic profile, a good score in any entrance exam like CAT/XAT/MAT/GMAT/SNAP will give you good chance to make into top B-Schools, Score around 85+ percentile is good enough to get top tier B-schools. If you are in final year of graduation you can try one more time giving CAT in 2018 and improve your score.

Chances are there, K.J.Somaiya generally look for the profile. Students with good profile able to clear the selection. A good academic profile or work experience will surely enhance your chances of selection. Generally, a score around 90-95 percentile is good enough to easily make into it. You need to perform well in the What-GD-PI process. Put your focus on the next round of selection once you get the call. Good Luck :).

At this score, you can look for ITM-Navi Mumbai, K.J.Somiaya (chances are less), Welingkar, ICFAI Business School, S.P.Jain - a call is based mainly on the academic profile/ work profile of the student. Based on K.J.Somiaya has a good placement record, average package is around 8-9 LPA. After that SIES and ITM-Navi Mumbai has around 5-6 LPA than Welingkar. Average offers do vary over the years. Check the below link for the comparison:
Https://http://shiksha.com/resources/college-comparison-11644-113283-160351-110946.