Fralia Grey-Mane in Whiterun won't sell anything because she is sad about her son. I saved and followed her to another cell. Then, the news. Her son, in fact probably all grey-manes, is a stormcloak supporter. Will there be an opportunity to get her son ( thorvald or something ) killed during the mission?

Is this the guy...

Yes. Sorry dude but I don't think you can purchase anything from her until you finish her quest(which leads you far up the map). After you accept the quest however, I'm still not certain. I'd suggest not talking to her if you only get two speech choices when she complains about her son. Travel to Markarth, or even better, to riften and find that nice fellow argonian who sells jewelry. He is pretty cool, and I'm not much of a fan of lizards.