Use the comma in all your cases, as the quoted phrases are in apposition to excuse/question/etc:
Many have an excuse,"I am not good at English." To the question, "Is your English getting better?" he answered, "Yes, it is." However, the excuse, "I am not good at English", is not...
Based on my understanding this are possible, although it is quoted from what someone else has said. I think when someone sais something is a quoted phrase, it is not limited to instances of rewriting what someone has said.
The expression "I am not good at English" is just as correct as "I am not good in