It depends. Downsampling and image pyramids are common. You might call it "filtering", which is more descriptive way of putting it. You ideally filter out the data you don't want (noise, specks of dirt) and keep the data you do want (letter shapes). Extreme blurring, used in obfuscation, is supposed to completely remove the part of the image you're supposed to hide, but in fact, the filter is not perfect. It only lowers the signal level, and you need a more powerful filter to extract the signal afterwards, and you end up with more quantization noise. ("Deconvolution" really just means coming up with the opposite filter.)

Deep convolutional networks (which are used here) are basically custom image kernels, non-linear activation functions, and simple downsampling algorithms chained together. So you don't really need to explicitly blur, because the network will train itself to use a blur filter if its necessary.

Resizing to a fixed size is a common first step in deep learning approaches, but that fixed size is generally large enough to keep a lot of image data. They don't usually pixellate down to 8x8 or whatever it is that the mosaic filter gives you.

I think it's generally a blur, as opposed to pixelation.

It says "mosaicing (also known as pixelation)".