Does the image size impose a limit on the number of convolutional layers in a neural network?

Question

Python

Good afternoon!
While studying convolutional networks, I came across a very popular Tutorial on training convolutional networks using a well-known example from Kaggle (cats vs dogs)
There, images (cat or dog) with the size IMG_SIZE=50 pixels are fed into the network, where the height and width are equal to each other and equal to 50 pixels
My question is the following piece of code Question 1. How can 6 convolution layers (filter size =2 ,padding =0 ,stride =1) and max_pooling (kernel size =2) Input_image

be applied to a 50 x 50 pixel image
(50x50)-->conv1-->(48x48)-->max_pooling(24x24)-->conv2-->(22x22)-->max_pooling(11x11)
That is, after the second layer, the size of our image becomes 11x11 pixels, and after conv3, the size becomes 3x3 pixels. How can we still apply the 3 remaining convolutional layers to such a small image?
Question 2: Why, after we have received 64 convolutions, only 32 filters are applied to them and not 128?

Answer 1

Here, a task similar to yours is analyzed in detail, even the size of the input image:
https://habr.com/post/348000/