"No, I do not know the ticket price." I know perhaps the author wants to highlight the genative case, but if a phrase is in common usage, why is it invalid?
This sentence does sound a little less common to me, but not wrong. I'd report it.
Just because that never makes sense in English. We'd never say "a price", I guess because you only pay one price.
"I do not know the price for one ticket", "I do not know the price of the ticket". I think these are better English.
Why not "one" instead of "a" in this sentence? The person might know the bulk price of 5 tickets, but not of one, so he could be specifying the quantity...
First of all, this isn't something one would normally say in English. It's fine grammatically sounds a bit strange. One ticket is already implied when you hear "a ticket." The only context I can think of where "I'd like to know the price of one ticket" might be appropriate is if you're specifically asking the ticket seller, and he replies, "Sorry, I don't know the price of one ticket." (In which case I'd say he's probably not very good at his job.) This sentence sounds more like part of a conversation among friends, or perhaps a result of asking some random person on the street.
Also, the original Russian doesn't include the requisite form of один, which I believe should be "я не знаю цену одна билета," so we wouldn't expect to see it in the translation either.