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 

• During the initial 15 minutes, deliver 2-3 strong points
• Present the problem in a crisp manner
• Support your points with real-life examples or that from current affairs. Supporting your own or even others' points through reasoning and examples will get you free points
• Summarize all the good points given by the others on a sheet of paper to give a nice ending note
• Give chance to the silent speakers this might impress the panelists
• Add recommendations and support it with relevant information 

Personal Interview 

• Know about yourself like your abilities, strengths, and weaknesses and present it in a good manner
• Practice the interview with someone and receive feedbacks
• You should prepare on personal information, education background, work experiences, hobbies, interests, future plans, and current affairs.

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.