Yes, submit your change of address immediately. Although it may not have any consequences, technically you have violated immigration regulations. But have no fear, they will probably just look the other way.
You have to provide the insurance information. That does not mean that they will be successful against you in the underlying case, but if you fail to provide the requested information pursuant to statute, they could have a separate cause of action against you. Additionally, your insurance company has a duty to defend you, so you should just turn the letter to your insurance agent.
With the limited information you have provided it is difficult to asses whether the State's case is strong enough for a conviction. Meanwhile, you should be aware that testimonial evidence is legally sufficient for a conviction; what you should do is hire a competent criminal defense attorney to investigate and advise you properly. Good luck.
Don't waste your time suing criminals, for one, their activity is not covered by insurance, and two, if they are engaging in criminal activity, they likely judgment-proof. What you could do is make sure to tell the prosecuting attorney to make it a condition of any plea offer to them that you get paid for your losses. You may even be entitled to compensation from the victims' fund. Good luck.
I believe you're omitting crucial information. Did she endorse the check, did she know about your claim? Answering these questions will be important to determine whether she is entitled to a portion of your settlement, which I believe is what you want to know.