Yes to one, No to two. If the ticket was received and paid, she pled guilty to speeding. If she was never in custody, the second doesn't apply. A good rule of thumb...if she wore handcuffs, even briefly, she was detained and it will show up if someone looks at the report.
A speeding ticket is generally not a criminal charge, it's a civil offense. If you pay it, you're done.
Attach information about the traffic ticket. Prove it was paid. Consider pulling a driver's record proving it was paid (or at least no one has a bench warrant out for her arrest).
$500 seems like a lot so make sure it doesn't include anything like reckless driving that *would* constitute a misdemeanor.
I'm still not going to post the attorney's firm that did the research, but search "N-400 speeding ticket" and you'll find it.
*Do Not* skip it. You've gotten this far, and you almost have the naturalization certificate in your hand. Don't drop the ball before you score.
I have no advice about the child support question.
Regards,
Vicky's Mom