Should I set feature extractor to eval mode when fine-tuning?

I am fine-tuning an ImageNet pretrained network on my own dataset. I have replaced the last fully-connected layer with the one that matches the number of classes in my dataset. And I have frozen the rest of the layers, which I consider as feature extractor. Now, I have two questions, that I think are somehow related to each other:

  1. The feature extractor contains some BatchNorm2D layers. So, should I set it to eval mode during training?
  2. How to normalize the input? Using my dataset statistics or ImageNet’s statistics (mean=[0.485, 0.456, 0.406] and std=[0.229, 0.224, 0.225])?

Thanks in advance.