Colleges in Madhya Pradesh

You should only appear for CET to get BHMS seats.

It depends in which department you want to apply to. If you have surpassed the registration date, then you might want to pay a visit to the campus and have words with the authorities personally. They do give admissions though even if you cross the deadline.

Cut off in AIR doesn't really get affected much but you can always wait for last round of counselling. It may go down if students leave the college after first round.

http://www.targetadmission.com/colleges/1232-shri-gs-institute-of-tech-science-indore#fees
You can get idea of fee structure by this.
Normally, closing rank for general category students is 35000-40000.

You probably will get MANIT if there isn't a top 20 percentile criteria. Make sure that you fill the JoSAA entries and have some alternative as a backup too.

If you are an Indian resident then you can give CAT entrance exam. If you are an NRI then you can apply using GMAT.
IIM Indore gives different weights to 10th, 12th, CAT exam in the selection of candidates for its MBA programme. You can check them here: http://www.iimidr.ac.in/academic-programmes/post-graduate-program-in-management/pgp-indore-admissions-details/

CAT is held every year around the month of November. It contains 3 sections namely, quantitative aptitude, data interpretation/ logical reasoning and vocabulary part. You need to clear different overall cutoff and sectional cutoffs for different business schools. It is a relative exam which means that your performance is judged in comparison to the performance of other candidates.