However, I would never invite a female student to my apartment on her own, it's just too risky. Plus the fact that I'm old enough to be their father and any "romantic" relationship would be a deceit. Whether we like it or not, we are guests in this country and our behaviour is noted by some, including other foreign teachers who might want to "shop" you if it suits them.

I think in the same way as you re what you've said above. However, I should add that I tell my students that they are welcome as girls, only if they don't come alone. However, I don't mind a boy coming alone. But I tell them they must call me first if they would like to come, as I prefer not to entertain unexpected guests. If I'm free, I'll be happy to see them in my flat. If not, I'll make an arrangement on the telephone to meet them another time at the time they called me.
FT's who are disingenuous and who will shop you to elevate themselves in the eye of the employer do exist. Be wary of all of your fellow FT's until you have gotten to know them. Be especially careful re lending them money. Some of them are a right motley crew, especially those teaching in the big cities of China!