traveling inJuly, are shorts o.k. or are they frowned on for adult women?

No, the shorts are accepted by woman there and you can see many people wear it in summer.

How about the length of shorts for teenage girls? Many here wear very short. Also how about tank tops with skinny straps?

During very hot days, Chinese girls also wear very short. Don't worry!

As for tank tops, in some busy and modern places, such as Beijing, Shanghai and Guangzhou, there are some girls wearing that with skinny straps as well. In other places, it is not generally acceptable.