Way to customize the width of the header for the icon as a case property column

For this, you can leave the Case Management tab as "does not use cases." This controls the cases of the case type you've selected in your module.

The User Case will automatically be loaded into your form when you choose a form that has User Case setup.

One way to accomplish this is by loading the label text in a hidden variable's Calculate Condition and then reference that variable later.

Create a hidden variable with your label text

Add the label text to the Calculate Condition of a hidden variable question type. For example, my_label_text

Reference that variable in a question's label text box

You can drag and drop that hidden variable, my_label_text, into the label portion of the question:

Save the hidden variable to a case property

You can then add logic to save my_label_text as a case property in the Case Management tab. In your scenario you may also want to add logic to save whether or not the question was answered properly.