Its normal, dont be alarmed just yet. If you received something from immigration beside an approval hire an attorney. Do you have anything to be concerned about (I mean your background check?). Good luck!
I suggest contacting few attorneys, ask friends and family if they know one. You can also google the attorney you go for a consultation and read the feedback. You have to make this decision hire someone you feel comfortable working with!
You should be able to travel. If you received a receipt letter extending your status for a year. Take the Notice you received and your green card with you.
Note there is always risks associated with travelling, I dont know the specific details about your case, but I had many clients travelling the same way.
Hope this helps.
Be carefull with making any reports. In fact how sure are you that she didn't apply for some sort of benefits and I suggest that you not file any false reports and why would you want to so spiteful. Let immigration deal with people that are out is status it is not your job!