I had a quick look and what you are trying to do (at least in the first 2 groups) should be possible with subquestion relevance. However: I don't think it is a good solution to have these two questions that depend on each other on the same page, because your respondents will see subquestions appear and disappear, which I personally prefer to avoid, as it gives insights in the structure of the questionnaire and it might lead to respondents playing around, etc. If they don't see the dependencies, they generally don't search for it, but when they see it, some will start to tinker around.
OK, here to the solution of your problem:
Group 1: You need to put Q1==1 into the relevance equation of the subquestions 1, 2 and 3 for Q2. See attached LSS file. Tested and works, even with both questions on the same page.
However, what happens if someone says "no answer"? Shouldn't then the whole question Q2 be hidden? I would actually not offer "no answer" here at all.
Group 2: Here you are trying to hide those options in Q4, that have been chosen in Q3. This also can be solved by adding a relevance equation to the subquestion relevance. You basically need to check if each subquestion in Q3 has been ticked in order to hide the corresponding subquestion in Q4. This code does the trick for the first subquestion. the others need to be adapted accordingly (see attached LSS - tested and works):
Group 3:
Would work similar to what we seen before, unfortunately the question type used does not offer subquestion relevance (because the question type does not have subquestions, but answer options). You might be able to do something with Javascript, but I am not sure how this would work. The only solution that comes to my mind right now is create two questions Q6, one with the first answer option, one without the first answer option and show them via question relevance, based on the fact if the first answer in Q5 was marked or not. Maybe someone else has a better idea.
Group 4:
Same problem as in Group 3. The question type used for Q8 does not allow subquestion relevance. You could again create the workaround mentioned above with two different questions and show one if one of the first 3 options in Q7 have been marked, if not, then show the other question.
Or, you could use a multipe answer question, and limit it to 1 answer. Not the cleanest approach, but works out of the box. Maybe someone else has a cleaner idea here.
How I miss answer option relevance...