in case my CC does not work in the UK at the self-service ticket machine, is there a place at Victoria Station where I can buy train ticket with cash (British Pounds, of course)?
You can use your CC at the ticket windows...cash is also welcome there. If you know your itinerary, you may want to check out some web bargains at nationalexpresseastcoast.com. Their website accepts American CCs.
I am stretching my memory -- but don't the trains for Dover leave from Liverpool or maybe Waterloo.
You can catch trains for Dover from Victoria, Waterloo, London Bridge, and Charing Cross stations. The fastest are from London Bridge and Charing Cross stations (saves about 1/2 hour).