yes, it's possible, but first make sure it isn't a virus or malware. if you have a security program, run a scan. if not, you can download microsoft security essentials for free
Yup could do that for now just to see if it catches anything. But to be honest with the severity of what she is worried about I would do nothing less than reinstaling the OS to make sure 100% that there is nothing using the mic/webcam or keyloggers on the computer. And this is just due to the nature of the situation.