How can I set for the username and password to be automatically created for new users?

You can do this from the WooCommerce options, going to WooCommerce > Settings > Account.

I can’t see the checkout within the product page, why is that?

In order to see it, you need to add a product to the cart.

I tried, but the checkout still displays the same fields as before, why?

The quick checkout is only visible to new users. Try accessing it from an anonymous tab, logging out, or using a different browser.