Translation:This river is narrow, the other one is broad.
Not necessary per se, but you want to take the translation of meg into account, too.
If not sure my rule is to always report it, they can easily dismiss it if it's not correct.
Is the word "and" understood here? Would it also be correct to say "This river is narrow, and the other one is wide." ?
Regarding your second question, yes that would be correct. It would even be better to say "the other one" than just "the other" in English.
As for the first question, the "and" corresponds to "meg". This word can be translated as just "and", but it often (as here, used not to separate the sub-phrases but inserted after the second subject) has a connotation of introducing a contrast, as if saying "this river is narrow, and in contrast, the other one is wide".
Is that different from saying, ""Ez a folyó keskeny, hanem a másik széles." (If that phrasing makes sense, that is? :) )
Perhaps "This river is narrow, while the other one is wide" would be a good (if non-literal) rendering?
That's a good one, yes. :D My favourite take on meg is this one, because it also takes the postposition quality into account:
"This river is narrow, the other one, however, is wide."
I think hanem only works in a nem X, hanem Y "not X, but rather/but instead Y" -- your sentence doesn't have a nem, and "This river is narrow, but instead the other one is wide" makes no sense, either.
As mizinamo said, "hanem" doesn't work here, but you could say "de": "Ez a folyó keskeny, de a másik széles." But this shows a much stronger contrast than the original sentence.
How would one ask 'this is the narrow river, the other one is wide' The definitive article is used in the suggested translation. I'm wondering if that is not the best translation.
"This is the narrow river" = Ez a keskeny folyó.
That has subject ez "this" and predicate a keskeny folyó "(is) the narrow river", while Duo's sentence has subject ez a folyó "this river" and predicate keskeny "(is) narrow ".
Remember that unlike English, Hungarian uses a definite article together with demonstratives -- ez a folyó "this river" is literally more like "this the river".
(And thus ez a keskeny folyó could also mean "this narrow river", if there is a predicate after it, such as a verb or an adjective.)
Melyik is an interrogative pronoun (question word). It means "which" or "which one". You can use it on its own and attach suffixes to it, like "Melyiket eszem?" - "Which one am I going to eat?" or in combination with a noun, where melyik behaves like an adjective: "Melyik almát eszem?" - "Which apple am I going to eat?"
Ami and amelyik are relative pronouns; they are used to introduce relative clauses and can translate to "which" or "that", like in "Ez az a tojás, amelyiket kerestem!" - "This is the egg that I was looking for!"
As you probably have noticed, melyik and amelyik are related to each other. They both mean "which" and are used to single out something from a group. In the above example, there are multiple eggs the sentence could be about, but only one that strikes your fancy, so you use amelyik. The general rule is (always with exceptions, of course): if you mention a noun in the main clause that you want to single out, you'll use amelyik in the relative clause.
Ami is related to mi, meaning "what". This is a bit more abstract. Now it's not about single nouns anymore, but about concepts. Consider this:
- Azt eszem, amit latok. - I eat what I see. I basically eat anything.
- Azt eszem, amelyiket látom. - I eat the one that I see. I just see one thing and I'll eat that one.
Basically ami mainly translates as "what", while amelyik is more towards "which". The trouble is, though, that in colloquial speech the use of ami is bleeding into the realm of amelyik. It even happens in this course (which I personally find pretty awful). So going back to the egg example, chances are that you'll frequently hear "Ez az a tojás, amit kerestem!" But it's not really correct.
vvsey also talks at length about this topic in this comment thread if you're interested.