Answers to your questions, in order:
(1) Yes, but if you're having the survey programmed in another software, they could just add the DR none question; choosing "Dual Response None" in Lighthouse Studio tells it add the DR question but it has no effect on the design (but you will need it checked for your analysis).
(2) Yes and the only difference is that after every CBC response you'll have the DR response (1 for yes, 2 for no)
(3) Yes, everything is the same
(4) Yes, your assumption here is correct.