Preparing for the CD PI round is a crucial part because your chances of admission depend on them largely. My answer entails the tips one must adhere to before and during the Case Discussion round.
Before Case Discussion
Be well versed in current affairs, general knowledge and industry trends.
Prepare arguments on some specific topics including both sides of the argument
Prepare concise but concrete points
Mock discussions are the most precise way to prepare for CD
Analyze your own performance relentlessly and keep improving
During Case Discussions
Personal Interview
Mock CD and PI are extremely important as the advice and feedback received will increase your performance and confidence tremendously.
Coming to the second part of your question, Both colleges have different merit lists. If you don't do well in NM Mumbai rounds, you still stand a chance to convert your NM Bangalore/Hyderabad call, provided you’ve applied for a PGDM course as well.