Рыбу нельзя перекармливать.

Because рыбу is the accusative singular form of рыба.

In this sentence, рыбу is the direct object of перекармливать (to overfeed), so Russian uses the accusative case.

• рыба = nominative singular (a fish / fish as the subject)
• рыбу = accusative singular (a fish / fish as the object)

So:

• Рыба ест. = The fish is eating.
• Кормить рыбу. = To feed the fish / fish.

Рыбу is singular.

Russian often uses the generic singular when talking about a whole class of things in a general way. So рыбу нельзя перекармливать can refer to fish in general, not just one specific fish.

This is similar to English sentences like:

• You shouldn’t overfeed fish.
• The elephant is a large animal.

Russian does this very naturally with singular nouns.

This is a very common impersonal Russian structure.

The word нельзя means something like:

• it is not allowed
• one must not
• you shouldn’t

So the sentence does not name a specific subject. It means something general like:

• One must not overfeed fish
• You shouldn’t overfeed fish
• Fish should not be overfed

Russian very often leaves the subject unstated in this kind of rule, instruction, or general advice.

Here нельзя expresses prohibition or strong advice against doing something.

With an infinitive, нельзя + infinitive means:

• must not
• should not
• it is not allowed to

So:

• Нельзя курить. = No smoking / You must not smoke.
• Нельзя шуметь. = You must not make noise.
• Рыбу нельзя перекармливать. = Fish should not be overfed / You must not overfeed fish.

Depending on context, English may translate it more as a strict rule or as practical advice.

Because перекармливать is the imperfective form, and that fits a general rule or repeated action.

• перекармливать = to overfeed (imperfective)
• перекормить = to overfeed once / to end up overfeeding (perfective)

With нельзя, the imperfective often sounds more natural when talking about:

• general habits
• repeated behavior
• rules and instructions

So Рыбу нельзя перекармливать means roughly:

• Fish should not be overfed as a general practice

If you used перекормить, it would focus more on a single completed instance of overfeeding.

The prefix пере- often adds the idea of too much, over-, or excess.

So:

• кормить = to feed
• перекармливать / перекормить = to overfeed

In this verb, пере- gives the idea that the feeding goes beyond what is healthy or appropriate.

So перекармливать is not just feeding, but feeding too much.

Yes, Нельзя перекармливать рыбу is also correct.

Both word orders are grammatical, but they differ slightly in focus.

• Рыбу нельзя перекармливать.
  Puts fish first, making it the topic or point of emphasis.
• Нельзя перекармливать рыбу.
  Sounds a bit more neutral, like a plain rule or instruction.

Russian word order is more flexible than English, so moving рыбу to the front helps highlight what is being talked about.

Not normally.

In this sentence, нельзя is most naturally understood as:

• must not
• should not
• it is not allowed/advisable to

So the usual meaning is:

• You shouldn’t overfeed fish
• Fish should not be overfed

It does not usually mean that overfeeding fish is impossible.

English often uses a passive here (fish should not be overfed), but Russian commonly expresses the same idea with an impersonal active construction:

• Рыбу нельзя перекармливать

So even though the English translation may look passive, the Russian structure is not a true passive sentence.

It is an infinitive.

After нельзя, Russian typically uses the infinitive:

• нельзя делать = must not do
• нельзя говорить = must not speak
• нельзя перекармливать = must not overfeed

So the basic pattern is:

[object] + нельзя + infinitive

That is a very common structure for rules, warnings, and general instructions.

It can be either, depending on context, but here it most likely sounds like practical advice or a care instruction.

With animals, health, food, and instructions, нельзя often means:

• you really shouldn’t
• it’s bad to
• don’t do this

So in a pet-care context, Рыбу нельзя перекармливать sounds like:

• Don’t overfeed fish
• Fish shouldn’t be overfed

It is strong, but not necessarily legalistic.