I am typing a question and answer transcript with quoted text messages. Do you include all the original punctuation? This is how I did it. Please tell me if this is correct.

Q. You do not perceive your response, "Are you really asking me that???? Harrassment!!!!!!!!!!!!!!!", as carrying with it sexual innuendo?

And another:
Q. And on October 7, the text of that is your comment, "OMG, maybe they really are out together today?!?!?!?!?! They are pretty tight!! LMAO"; is that right?

Yeah, that's fine. If someone makes a mistake in their text or whatever you're quoting, you can use [sic] to show it was as they typed/said it.