Hi,there
October is the best time to visit Beijing, neither too cold nor too hot.
Look at this page for the train schedule from Beijing to Shanghai:
https://www.travelchinaguide.com/china-trains/display.asp?tp=1&to1=
Shanghai&from1=Beijing&tstop=&trainno1=
The trains leaves from either Beijing Railway Station or Beijing South Railway Station to Shanghai Railway Station.
It also tells the price and travel time based on different trains and seats.

I also intend to go to Beijing this October. Can I possibly confirm my bookings of itineraries with travelchinaguide without having to pay thru cash transfer or credit card before my actual trip? Also, do you have itineraries excluding hotel? Thank you!

You could make payment in other ways, like Paypal and Western Union.
For the itinerary, we could offer tailor-made tours as per your request, if you would like to arrange the hotel on your own, we will deduct the hotel price for you.
Please choose your preferred itiernary to submit the online enquiry, so that we can offer you the details. Thank you.