CAT

Yes, CAT is difficult but not that it is impossible. With proper utilization of time and some hard work, you can score a good percentile on it. And starting its preparation depends upon your own advantage.

You can try colleges in Pune some private colleges the fees will be Rs 5~7lakhs

The weights assigned are changed every year. For PGP16-18 course, please refer to the link.
http://cdn.iimkashipur.ac.in/media/admission/Admission_Policy_16_18.pdf
Yes it is possible provide one compensates for those in other areas such as WAT/PI

Actuarial Science

CAT is one of the toughest exam for MBA admissions in IIMs and many other MBA institutes.You have to be good in all your concepts and study hard. Go through the previous year question papers and try to solve them, then you will understand where you have to improve and where your strength lies. Practice and study hard.
All the best.

The total tuition fee for 1 year is Rs 2,75,000, which makes the total tuition fee Rs 5,50,000. No, CAT is not necessary, however you are required to write a SRMCAT entrance exam.

Yes, possible. The specified cut off is 85 percentile. The net aggregate of your academic and non academic profile is considered and hence you could be considered for the call.