The mandatory setting itself cannot be changed via conditions or Expressionmanager.
When using conditions, you could just copy the question and set one question to mandatory. Depending on the condition you show one question (one with or without the mandatory setting). That way you end up with two response fields for one question.
If you want everything in one question, you might use Expressionmanager and do a validation expression in the second question to enforce and answers to that question.
You can learn more about Expression manager here:
www.limesurvey.org/manual/Expression_Manager
The noanswer button is not shown in the second way. You're better off creating such fields inside your question.
Depending on your LimeSurvey version you can use relevance on subquestions.
