As per the image, its completely read only.
even the attributes are not customizable, like from business required to not required.
So to make it customizable, just hide the existing Resolve Case button and put your own and on click call your own cusomt page(aspx or silver light page) and in that page you can put your fields to be captured.
But while doing so, you can not capture the record in Closed Activities in the case.
There are work arounds, u can make the enity editable to true in the DB, but risks are there wt can it do.
to do so, do not delete existing fields, just hide it and pass some default values and use ur custom fileds on for to capture the values.
You can customize the Views, so ypu can put yoyr colummns.