How to hide core fields in Content types?
There are two ways you can do this.

You can do this with permissions for some items. 'Menu settings' is controlled by 'administer menu' permission.

If some item is being put onto the page which can't be controlled by permissions then you can use a form alter hook to remove them. I tend to set #access to false rather than completely removing the item from the form. 

There is a big explanation of examples of how to alter forms here