Are my steps correct for a proper classification of a sick brain? I have a dataset with MRI of patients with a specific disease that affects the brain and another dataset with MRI of healthy patients.

I want to create a classifier (using neural networks) to classify if the MRI of a new patient shows the presence of the illness or not.

First of all, I extracted the brain from all the MRIs (the so-called skull stripping) using BET tool found in FSL.

I have three questions for you


As the input to the training phase, I want to give the whole extracted brains (possibly in the nii format). What kind of preprocessing steps do I need to apply once I've extracted the brains (before passing it to the classifier)?
Do you know any better tool for skull stripping?
Do you know a tool (or library) that takes as input a nii files and allows me to create a classifier that uses neural networks?
It looks like everything you want is available with the Deep Learning Toolkit (DLTK) for Medical Imaging

There is also a blog: An Introduction to Biomedical Image Analysis with TensorFlow and DLTK

There is a DataCamp course that walks you through most of the process but instead of a classifier they use deep learning to reconstruct brain images.  They provide a link to their MNIST classifier example which should be easy to adapt for your purpose.  See: Reconstructing Brain MRI Images Using Deep Learning (Convolutional Autoencoder)

ResearchGate has a thread that may help:
What is the appropriate way to use Nifti files in deep learning?