At Hangzhou Airport, you could take a bus to reach downtown Shanghai directly. The bus info could be read on this page: https://www.travelchinaguide.com/cityguides/zhejiang/hangzhou/airport-transportation.htm

If you miss this bus on daytime, it is suggested that you take the shuttle bus to Hangzhou Railway Station firstly and then transfer to Shanghai by train. This should be the most convenient and cheapest way except of the direct bus.

Yes, please wear your warm down jacket since both of Shanghai and Hangzhou are humid and cold in Nov although no snow will happen.

As for shopping, what kind of goods are you looking for? Usually, there is seldom sale promotion on early Nov.