CMAT

Here're the best colleges through MAT & CMAT:
MAT Colleges:
SCMS Cochin,
MS Ramaiah Bangalore,
Alliance Bangalore,ICFAIUPES Dehradun
CMAT Colleges:
IFIM Business School, Bangalore
Christ College, Bangalore,
UPES Dehradoon
Jaipuria Institute of Management, Lucknow
PSG Institute of Management, Coimbatore

Correspondance B.Com degree holders are eligible to appear for CAT, MAT, XAT etc entrance exams for admission to MBA.

I can't say about other college but try for B.K. School of Business Management. You have good chance of getting into bk. Last year till 70 percentile students with SEBC got admission in this college. So you have a bright chance.

Most of the Universities and Colleges consider these exams for admission but there are some private Universities lIke amity,sharda etc may or may not consider these exams as there are two category for admissions I) sponsored and ii) non-sponsored

Your admission is depends upon on cut off marks of Cmat exam and your score is average so there are 65% chances of getting admission. The cut off marks are 85 to 90 to get admission.

You can refer this link: https://www.shiksha.com/mba/colleges/mba-colleges-in-lucknow

Yes chances are good. Keep yourself updated with recent ACPC announcement. Last year admission was stopped at 175 score but it varies few marks every year so you have good chance to get selected.
Thanks

CMAT you have to score 70% or more to get admission, or else you can write AMAT (Alliance Management Aptitude Test), and in that also if you score good marks you will get admission, you just visit alliance.edu.in and apply for the interview date and if you are through in that you will get admission.

Yes lots of government institutes are there but only by CAT or CMAT. You have to score much better for getting a good government college and by 70+%ile in CAT you will get lots of government college but you have to face GD/PI.

Yes, there is negative marking in exams you mentioned above.