Can I still plug in the receiver with the phone case on?
Generally no problem, unless your phone case is too thick. My phone case is relatively thin and I have no problem using it.
Does this ulanzi J12 microphone work with iPhone 12 pro max?
Yes, of course. It is lightning interface and uses iPhone and iPad.
Does this wireless microphone have noise cancellation?
Yes, it has professional noise reduction module processing, and the recorded sound is clearer.