Ako sutra ostane losos, ponijet ću ga na posao za ručak.

Because Croatian normally uses the present tense after ako for future conditions.

So Croatian says:

• Ako sutra ostane losos, ...

not:

• Ako sutra će ostati losos, ...

This works a lot like English:

• If there’s salmon left tomorrow, I’ll take it...
• not If there will be salmon left...

The future meaning is already understood from ako plus sutra, so the verb in the if-clause stays in the present.

Ostane is the 3rd person singular present form of ostati, meaning to remain, to stay, or to be left over.

Here it means something like:

• if salmon is left over
• if some salmon remains

The subject is losos, so ostane is singular.

Croatian is paying attention to aspect here.

• ostati → perfective
• ostajati / ostajati or ostajati / ostaje-type idea → imperfective

In this sentence, the speaker means a completed result:

• after eating, maybe some salmon ends up left over

That is why ostane sounds natural.

If you used ostaje, it would more likely suggest:

• something habitual
• something ongoing
• something that keeps being left

So:

• Ako sutra ostane losos... = If there’s salmon left tomorrow...
• Ako sutra ostaje losos... would not fit this situation as well.

In the given sentence, losos is in the nominative because it is the subject of ostane.

Croatian structures this as:

• the salmon remains / is left over

So losos is the thing doing the grammatical action of remaining.

That said, you may also hear:

• Ako ostane lososa...

That uses the genitive, often with a partitive sense, meaning:

• if there is some salmon left
• if any salmon remains

So the difference is roughly:

• Ako ostane losos = the salmon / the salmon portion is left
• Ako ostane lososa = some salmon is left

Both can be natural, but they focus a little differently.

Ponijet ću is the future tense of ponijeti.

Croatian future is often made with:

• the infinitive
• plus the auxiliary ću

With infinitives ending in -ti, when ću comes after the infinitive, the final -i drops:

• raditi → radit ću
• ponijeti → ponijet ću

So:

• ponijeti + ću → ponijet ću

Another very common order is:

• Ja ću ga ponijeti na posao.

That means the same thing.

Because ponijeti is a perfective verb for a single completed action: taking something along somewhere.

Here the speaker means one specific future action:

• tomorrow, if there’s salmon left, I’ll take it with me to work

That is why ponijeti fits well.

Compare:

• ponijeti = to take/bring along once, successfully
• nositi = to carry, to be carrying, to carry habitually/repeatedly

So ponijet ću ga sounds like:

• I’ll take it with me

while nosit ću ga would sound more like:

• I’ll be carrying it
• or I carry it regularly, depending on context

Because Croatian often drops subject pronouns when they are not needed.

The verb form ću already tells you the subject is I:

• ponijet ću = I will take

So adding ja is possible, but not necessary:

• Ponijet ću ga na posao = neutral
• Ja ću ga ponijeti na posao = more emphasis on I

Croatian does this all the time, unlike English.

Ga means it here. It refers back to losos.

It is a short unstressed pronoun, called a clitic. Croatian clitics usually go near the beginning of the clause, in a fixed-ish position.

So:

• ponijet ću ga na posao

is natural.

You can also say:

• Ja ću ga ponijeti na posao.

But you normally would not say:

• Ja ću ponijeti ga...

because the clitic ga does not usually go at the end like English it does.

Also, even though ga can mean him in other contexts, here it clearly means it, because it refers to salmon.

Because na posao is the normal Croatian expression for to work.

Croatian says:

• ići na posao = to go to work
• biti na poslu = to be at work

So in this sentence:

• ponijet ću ga na posao = I’ll take it to work

By contrast, u posao usually means something more like:

• into the work
• into the task
• into the business/activity

So for the everyday destination work, the idiomatic choice is na posao.

Za ručak means for lunch or as lunch.

It tells you what purpose the salmon will have:

• the speaker will take it to work to eat for lunch

This pattern is very common:

• za doručak = for breakfast
• za ručak = for lunch
• za večeru = for dinner

So it does not mainly mean during lunch time. It means the salmon will serve as the lunch meal.

You could, but it changes the feel.

• ako = if
• kad = when

So:

• Ako sutra ostane losos... = if there happens to be salmon left
• Kad sutra ostane losos... = when salmon is left tomorrow, with more expectation that this will happen

In your sentence, ako is better because the speaker is talking about a possible condition, not a certain event.