People usually say : What's the weather like in Shanghai? If you live in a region north of Shanghai then you can say: How is the weather down in Shanghai? [ meaning in the southern direction down from your region]

When you are somewhere in the North of Shanghai, using 'down in Shanghai' refers to it being in the South of your location. If you are in another country for example or continent, you wouldn't ever use ' down in Shanghai'. That is a very specific expression indicating location. 上海的天气怎么样 means "How is the weather in Shanghai?" It is not the same as 'down in Shanghai' and I don't know how you could express that in Chinese ( a native could help).

Yeah, they are the same.

上海的天气怎么样？可以代表这个意思。如果你在上海的北方你能用“down in shanghai",如果你问这个问题的时候你在上海的南方可能听起来有一点怪，但是别人会明白你的意思。