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Being a subject matter expert will certainly help a good project manager but it is not a prerequisite for his/her success.
Yes,being a project manager you must have the subject knowledge of your project !
The project manager should have the knowledge that make him aware of all project areas
Not really necessary
I think being SME can help you getting respect from the Project team. You can use it to manage the project more efficeintly. Also, you can identify potential issues more quickly as you are happen to be a SME.
However, if you have an excellent and motivated team then your team will help you resolving the issues and you can just focus on the Project Management activities. In this case being SME won't give you much of the benefit.