My professor invited me to his house, should i go or not? (sorry,don't know which category to put)?

I must admit that it is a little strange for an elderly divorcee to invite a young female to his home without suggesting you bring a friend or two with you. Perhaps he really is curious about your views on Chinese culture, and felt you'd feel as comfortable in his home as he does. Thus, to him, there may be nothing untoward about it. When I was younger, I'd visit elderly people in their homes upon receiving an invitation. I found them to be very good converstionists, and nothing unsavory ever occurred or was even suggested. Perhaps he is just old-fashioned and enjoys offering hospitality to someone who he believes would understand such politeness. Then again, he could be a pervert. To test this out, ask him if there is a public place where you two could both feel comfortable chatting. If he insists on going to his home, then you must insist on bringing a friend or two with you. Suggest a small group luncheon to encourage an expresssion of his hospitality.