Chapter6 minibatch_std_layer function

[youngsend]

Dear Authors,
I have several questions about the minibatch_std_layer function.
1.original code:
# Calculate the standard deviation over the group [M,W,H,C]
minibatch = K.backend.square(minibatch + 1e8)
Since here standard deviation should be calculated, I think this line should be
minibatch = K.backend.sqrt(minibatch + 1e-8)

2. original code:
   # Take average over feature maps and pixels [M,1,1,1]
minibatch = tf.reduce_mean(minibatch, axis=[1,2,4], keepdims=True)
   Why is axis=[1,2,4]?
   I think it should be axis=[1,2,3].

3. original code:
   shape = list(K.int_shape(input))
   Does "input" mean "layer"?

4. I do not understand why group_size is considered here.
   Can you please explain why group_size is necessary?