I'll try to help but as you already know I'm not an HST authority so my advice will be generic.
1) Soreness is no big deal. Warm up and train through it.
2) If the soreness is very severe meaning it will hamper your ability to train or possibly cause injury - do some very light concentric work and a bit of cardio to get blood flowing and ease recovery but a full workout is discouraged if you can help it.
3) A day off won't kill you but it's important to try to stick to the schedule as a program that is based off dual factor methodology (even though casualBB says it's not a typical dual factor progam in the way it's run) are accounting for a fatigue component so ideally the schedule remains intact.
4) If HST has some specific protocol or command regarding dealing with DOMS, I have no way of knowing that but I'm trying to offer you something before you go to the gym.