Hi, Jimmy,
The latest shuttle from Hangzhou airport to the railway station sets off at 22:30. Your flight will land at 22:00, so you may catch this last bus. Passing the luggage claiming area will also cost your some time. If you miss it, you have to take a taxi and that will cost you about CNY100. 40 minutes will be needed.
From Hangzhou to Shanghai, you don't have to take a night train. Otherwise it will be midnight when you arrive in Hangzhou because it takes 2-3 hours from Hangzhou to Shanghai. I recommend the bullet train D5472 08:19/10:02 and one first class ticket costs CNY76.00.
I believe that there are many hotels and hostels near the railway station both in Hangzhou and Shanghai.

There are many bullet trains from Shanghai to Suzhou. You even do not need to purchase in advance. It takes 34 min. And CNY32 is for one first class ticket.
There are also several bullet trains from Suzhou to Wuxi. But most of them start from Shanghai, So you had better buy tickets in advance.
The situation is similar from Wuxi to Changzhou. (I guess you mean Changzhou):). By the way, you can get all these tickets in Shanghai railway station. Anyway, asking never hurts, right?
In January, it will be still cold in these cities. Maybe Hangzhou can be better. Still April and Setember is the best time to visit there.