MBA Ranking

Yes, it increases your chances but it is not necessary.
So, why do CFA or FRM? These are courses for individuals interested in specific fields. CFA (Chartered Financial Analyst) is for the ones who want to go in money/asset management. Those interested in equity research and analysis finds this course interesting. FRM (Financial Risk Management) is for those interested in risk management of various investments. So pursue these courses only if you want to go into that particular field and are genuinely interested. CFA takes almost one year for each level. There are three such levels. Only having level one will not help much for your career. During the interviews for admission it will surely sow your interest in finance as such. For CFA you need to put in lots of hours of study, so if you are not interested don't do it. Most of the students entering IIMs don't have a CFA. So it is okay not to have such certifications. Just go through the portions of the exam and see if you are interested.

It is because they profit highly from this or are controlled by powerful people.
Many of the local private MBA colleges are always looking for making extra bucks and what is better than giving backdoor admissions to students with rich parents. Such colleges profit highly from this and don't want to stop it. In some cases it is due to pressure from powerful people. Let's say there is some industrialist who gives regular donations of large amounts and one day he asks them to give his son admission there. If they deny it, they will be losing all the future donations from that guy. So they comply. In other scenarios the student may be in relation to some political leader or the committee of the college. The truth is most of these colleges don't try to stop backdoor entries. The more such entries the more profit for them.