Lost in negativity...
I'm having a hard time figuring out things like
Il n'y a qu'un seul moyen
It looks like "There's NOT (any) one sole way" to me... am I translating it wrong? If not, is there any equivalent structure in English (something like "There's but one way to do it")?
Or do I just need to say "That's the way it is in French" and memorize it?
'Ne... pas' would negate the verb, but here we have 'ne... que'. That means ONLY something. So it means 'there is only only one way', which is just reinforcing the only!
Basically, the structure is that 'ne...que' means 'only' with a verb.
So "il y a seulement ..." is pretty much the same thing as "il n'y a seule ...", then? Is the second one more emphatic, perhaps?
No. Il y a seulement... = Il n'y a que.... You can add the adjective "seul" to the object in the second sentence in order to emphasise it even more, like in the example you brought.
In the original sentence, seule is an adjective: the sole way, if you like. Then the verb can also be given an 'only' meaning, using 'il n'ya que'; they're separate parts.
My friend, those kind of sentences are not meant to be explained. Learn them by heart because they are used a lot in every day conversations. Even native speakers sometimes can't write them correctly. Just memorize how it sounds and what it's supposed to mean.