You have 10 days from the date of arrest to request a hearing with the DMV. If you did that, your license is still valid until a hearing takes place and the DMV rules to suspend to suspend. If your license is suspended, you'll have to wait 30 to apply for a restricted license with proof of enrollment in a drunk driver program.
That's right, you would only file a claim against the other driver's insurer. They have a duty to defend the driver and settle the matter if liability is undisputed. You would still need to report the accident to your insurance company. Also, if the other driver does not have enough insurance to cover your damages, your insurance would cover the difference if you have uninsured/underinsured motorist coverage on your policy.
If you weren't arrested, you don't have anything to worry. If the police showed up and gave you a citation, this constitutes an arrest. Also, if you weren't arrested, I suggest you do not pay anything. Civil demands have no legal force. The letter will probably threaten to sue you and/or report you to the authorities, but that's BS. I have never seen that happen. Good luck.
Your insurance company has a duty to defend you in this action, so you could let them handle it for now. Your insurance also has a duty to settle if liability is undisputed. That said, if your insurance fails to defend or the judgment exceeds the policy limits, then you may have something to worry about. You're name appears because you and your insurer are co-defendants. Whatever your insurance doesn't pay, you could be on the hook for.
You're lucky that you weren't arrested. This is not a fine - it's a civil demand. You don't need to pay. The threat to file a police report is just that. I've never heard of the store filing a report if someone fails to pay. These demands have no legal force, so you cam keep throwing these letters away. However, if you signed something promising to pay, this may be a binding agreement and they can sue you. Other that, consider yourself lucky.
If it turns out that she fabricated the whole thing, you won't need to do anything. The prosecutor decides whether or not to file charges, not you.
You could sue her in civil court for intentional infliction of emotional distress, among other things. If she doesn't have anything, it's not worth the effort.
As far the video, my colleague is absolutely correct. Show this to your attorney. It may be admissible, assuming that it can be authenticated.
Finally, these are difficult cases for...
It would be a mistake to handle this on your own. Although volitional movement is a requirement for a DUI conviction, that can be proved through circumstantial evidence. You have a case, but don't screw it up by going it alone.