Should I make formal complaint?

Neighbors are sticky! Talk to the landlord and see what reaction you get from them. Have you told the woman to mind her own business? I wouldn't answer any of her questions. I would say the same thing to every question she asks, "It's none of your business and I think it's rude of you to ask." If you're worried about her reporting you to housing, you should contact them first and let them know what's going on. If you aren't doing anything to break the rules, you'll be fine.