Hi, I'm afraid that you will miss the train either to Shanghai or to Beijing after 22:00. The last train to Shanghai leaves at 21:28 and the one to Beijing leaves at 22:58 (at least 1 hour is needed from airport to the railway station).

These three cities should be in hot summer. Hangzhou and Shanghai may be muggy due to the rainfall sometimes. Beijing is hot and dry but much cooler in the early morning and at late night.