I$\text{'}$m learning PyTorch and need help understanding some key concepts and best practices. Please provide detailed explanations and code examples for the following:

model.eval$()$ and torch.no$\_$grad$()$:

a$)$ What is the purpose of model.eval$()$ and how does it affect a neural network?

b$)$ How does torch.no$\_$grad$()$ work and why is it used?

c$)$ Should these be used together? If so$,$ why?

Data handling for training, validation, and testing:

a$)$ Is it necessary to shuffle validation and test datasets? Why or why not?

b$)$ How does shuffling or not shuffling affect model performance evaluation?

Please provide a comprehensive code example that demonstrates:

a$)$ Setting up a simple neural network model in PyTorch

b$)$ Preparing data loaders for training, validation, and test sets

c$)$ A complete training loop that correctly uses model.eval$(),$ torch.no$\_$grad$(),$ and handles data shuffling appropriately

d$)$ A validation loop that follows best practices

e$)$ A test loop for final model evaluation

Please explain each part of the code and why certain choices are made $($e$.$g$.,$ when to use model.eval$(),$ when to shuffle data, etc.$).$ Include comments in the code to clarify important points.