What does D.N.I. mean?
"The other alternative offered was o tarjeta de residente."
It should be address, but there is only one space to put it in the form.
If there is only one space, just a cross, but probably you might have to put the number of the card (either identity or resident)
Documento Nacional de Identidad = Identity card. In Spain native citizens have a DNI, which is document identified with a number of 8 digits. Immigrants have a "tarjeta de residente". I can suppose that in the form you have to put what kind of document you are in possession of with a cross. (if there is only one space).