How can I change the order of the fields?

Access the Settings page and scroll down to the "Visible Fields" section then tap the "More Actions..." row
Next tap the "Change Order of Fields" option
To change the position of a field, press the reorder control on the right, then while still pressing, slide the field into the position you would prefer
Once you have completed your updates then tap the "Done" row at the bottom of the list of fields