Question Diversion

Diverting from a question asked

See avoiding the issue and possibly red herring , depending on the direction of the diversion.

I'll try to be accurate with my fallacy classifications.

Example 1: 
John: If you really believe that Sarah is telling lies, then why are you re-telling her story Matt?
Matt: Sarah and I are friends and she's feeling bad because no one believes her.

Here's John's argument:
1. Matt knows that Sarah lies about X.
2. Matt is claiming X to be true anyways.
C. Therefore, Matt is being dishonest.

Here's Matt's response:
1. Sarah needs support.
2. Friends are supportive.
C. I will support her.

The question is diverted from honesty to being supportive. This is a red herring because the diversion has the intent of switching the discussion.

Example 2:
Same argument as in example 1 but with a different response.
Matt: Who are you to judge John?

Matt's response:
1. Only people with no mistakes, or very few mistakes, can judge dishonesty.
2. John is not a person with very few or no mistakes at all.
C. Therefore, I should be able to re-tell the story.

The argument is not actually diverted to another topic like in the previous example, but it's avoided all together by dismissing what John said. This is avoiding the issue. Note that the mechanism to avoid the issue is by providing an enthymeme: 

E: Since John is no one to judge, I can be dishonest.

Premise E would be close to committing the two wrongs make a right fallacy. I say "close to committing" because the definition technically would imply that the same action against Matt would have to be made.

Example 3.
Teacher: if you studied for the exam, then why were you asking for help? That's cheating!
Jenny: I didn't copy anyone! 

Teacher's argument:
1. Students that ask for help in an exam are cheating.
2. Jenny asked for help.
C. Jenny is cheating.

Jenny's response:
1. Only students that copy in an exam are cheating.
2. I did not copy in the exam.
C. I did not cheat.

Jenny changed premise 1 to get to her conclusion and therefore committed the strawman fallacy. The question was also diverted because Jenny skipped the question by distorting what was said.  

There's actually more to be said with this situation. It all depends on what Jenny meant to do. I just had a discussion on whether or not a fallacy of ambiguity fallacy is made if the hearer makes that misrepresentation on their own. For example, if Jenny honestly thought that by "asking for help" really means "trying to copy" (one might just be asking for clues while the other might be straight up plagiarism).

Example 4:
Teacher: Jenny, answer me this; why were you looking over to places, taping on Jonny's shoulder, and  whispering? 
Jenny: So, because I was looking over to places that means I'm a cheater? 

Teacher's argument:
1. If you look over to places on an exam, chances are that you are up to no good.
2. You were also taping on Jonny's shoulder and were whispering.
C. Adding these up, you were trying to cheat.

Jenny's response:
1. If you look over to places on an exam, chances are that you are up to no good.
C. Just because something is possible, it doesn't mean it's probable.

I'm phrasing Jenny's conclusion this way because I also just had a discussion on the appeal to possibility. I believe that in fact, that's what Jenny is accusing the teacher to be committing. But it works only because Jenny ignores premise 2 to divert the question. This would be selective attention.

What am I getting at? I think your question is valid if I understand it correctly: what kind of fallacies can there be by diverting questions? Many of them can be changed to argument form, so I guess your worry has to do more about locution. The way I understand locution is the manner in which phrases are said or expressed. 

As somebody already pointed out, we should also consider questions that seem to be fallacious themselves. The famous one is "have you stopped beating your wife?" With no context, this question might be begging the question. The questioner might be begging for the respondent to answer a presupposition without, perhaps, providing any support to that presupposition. So it is rational to divert it. 

Case in point, I recommend to frame your questions taking two things into consideration: is my question too broad and maybe I want to ask if any fallacies may arise? When is an apparent fallacy not fallacious; that is, are there any exceptions to the fallacy?