Is image resizing needed to training a new Yolo model?
(1) It already resize it with random=1 in .cfg file.The answer is "yes".The input resolution of images are same.You can resize it by yourself or Yolo can do it.
(2)If your hardware is good enough,I suggest you to use big sized images.Also as a suggest,If you will use webcam,use images as the same resolutions as your webcam uses.
(3)Yes, same as training.
I would like to train a new model using my own dataset. I will be
  using Darkflow/Tensorflow for it.

Regarding my doubts:
(1) Should we resize our training images for a specific size?
(2) I think smaller images might save time, but can smaller images harm the accuracy?
(3) And what about the images to be predicted, should we resize them as well or is it not necessary?