I have seen that は acts as a sort of negation (or contrast) particle, although I'm not sure how it works, for example:
1) わたし は ともだち が いません
2) わたし の ともだち が いません
Is 1) the only correct sentence? Why? And what's the rule for using は instead of other particles? I have tried searching a bit but I still can't seem to understand this.
Another example would be
1) さかな は たべません
2) さかな を たべません
Is 2) incorrect? Why? Are there any other cases where I should be aware of this?
When you describe a general fact, a sentence of statement needs some topic parts, in short, "I don't have friends" translates to わたしは ともだちがいない. ("My friend is not here" translates to わたしのともだちは いない as long as it's a general fact.)
On the other hand, what's newly discovered i.e "(emergency) My friend is missing!" is expressed without any topics as わたしの ともだちがいない.
Third, you can rephrase いないのは わたしの ともだちだ (it's my friend that's not here) as わたしの ともだちがいない, which is the same form as the above.
さかなは たべない can be (1) a reply to question "How do you treat the fish?" or (2) an implication that you may eat other things but not fish.
さかなを たべない is a reply to question "What would you save among these things". Edit: If you still say さかなは… instead, it implies that you anyway don't eat the fish and now the problem is what to choose from the rest.
No, は is the topic marker (i.e., it marks what the sentence is really about), and contains no connotation of negation/contrast.
In your first case, (1) means "I have no friends" and (2) means "My friends aren't here" (literally, "my friends don't exist [here]"). Both are correct, but they have very different meanings.
In your second case, (1) and (2) both mean "[I] don't eat fish". They have the same meaning because the object, 魚｛さかな｝, is exactly the topic of the sentence. However, if you're in some strange setting when you're concerned with fishes eating things, (1) can mean "[The] fish doesn't eat". But people rarely talk about fishes' eating habits.
In your second case, I think the xuq01's answer is perfect.
To help you understand the case perfectly, I'll show you some examples.
In Japanese sentences or conversations we often or usually omit words or phrases when they are well-known among the persons concerned, even when they are the subject of the sentence.
1) さかな は たべません
2) さかな を たべません3) わたし は 魚{さかな} を 食{た}べません - I don't eat fish.
4) さかな は 餌{えさ} を 食{た}べません - [The] fish does not eat food/bait.
5) わたし は 肉{にく} と 野菜{やさい} は 食{た}べます が 魚{さかな} は 食{た}べません - I eat meat and vegetable, but I don't eat fish.
The sentence 1) is usually said in the context like the sentence 5), and the sentence 2) means the sentence 3) by omitting the subject.
xuq01's answer:
However, if you're in some strange setting when you're concerned with fishes eating things, (1) can mean "[The] fish doesn't eat".
xuq01's answer may refer to the sentence like 4) for the sentence 1).
