"Not one tree stands next to the city, but two."
Translation:A város mellett nem egy fa áll, hanem kettő.
Oaok, your tree is not in focus in your sentence. Remember that the focus is whatever is in front of the verb, and that's "a város mellett" for you there.
If you want to negate a specific piece of information, you have to place it between the negation and the verb. In this case "nem egy fa áll" needs to stay like that, and you can place "a város mellett" in front or behind that.
Not really. The purpose of this sentence is to nail down the number of trees by the city, so the trees need to be in focus, i.e. in front of the verb. Your focus is on the city, which makes it sound like "It's the city (and not anything else) next to which not one but two trees are."
You can place áll behind fa or kettő in your sentence.