To add fields to the "Create Case" form you will need to add the extra fields to the CreateCase.aspx page in the code. Create a label and text entry field for which ever fields you would like to add and then wire them up in the code behind.
You can see examples of how this is done with the fields already created for the form. The fields get added to the CRM entity starting on line 43 of the "CreateCase.aspx.cs" file.
Adding additional columns to the "Vew Cases" gridview can be done from within the CRM. You can add additional fields to this grid by modifying the "Cases Web View" on the Case entity from the Customize Entities area of the CRM.
Hope that helps!