Čak ni poštarina nije u ceni.

Čak ni adds strong emphasis. It means something like not even.

So Čak ni poštarina nije u ceni means that the speaker is emphasizing how little is included: not even the postage/shipping cost is included.

• čak = even
• ni = not even / neither / not ... either, depending on context

Together, čak ni is a very common way to say not even.

Yes, it looks like a double negative from an English perspective, but in Serbian this is normal and required. This is called negative concord.

In English, you usually say:

• Not even postage is included.

In Serbian, if you use a negative word like ni, the verb also stays negative:

• Čak ni poštarina nije u ceni.

So ni and nije work together, not against each other.

Poštarina means postage or postal charges. In many real-life situations, it can also be understood more loosely as shipping cost, especially in sales contexts.

A useful distinction:

• poštarina = postage / mailing charge
• dostava = delivery
• troškovi dostave = delivery/shipping costs

So in some contexts, poštarina may sound specifically like postal postage, while a business might more often use dostava or troškovi dostave for general shipping.

Poštarina is in the nominative singular because it is the grammatical subject of the sentence.

The sentence structure is basically:

• poštarina = subject
• nije = verb
• u ceni = complement

So the sentence is saying:

• Poštarina nije u ceni = The postage is not included in the price

Because poštarina is the thing being talked about as the subject, it stays in the nominative.

Because the preposition u here means in / within, and in that meaning it takes the locative case.

The noun is:

• cena = price

Its locative singular is:

• ceni

So:

• u ceni = in the price / included in the price

This is a very common phrase in Serbian.

Yes, literally it means in the price, but idiomatically it means:

• included in the price
• covered by the price

So nije u ceni is a very common way to say:

• is not included in the price

A closely related phrase is:

• uračunato u cenu = included in the price
• nije uračunato u cenu = not included in the price

Because in the present tense, the verb biti (to be) does not show gender.

Here, nije is simply:

• 3rd person singular negative present of biti

So it is used with any singular subject:

• Poštarina nije...
• Paket nije...
• Cena nije...

Gender matters in some other forms, especially the past tense, for example:

• Poštarina nije bila uključena...
  Here bila and uključena are feminine.

But in the present tense, nije stays the same for masculine, feminine, or neuter singular subjects.

Yes. A few natural alternatives are:

• Poštarina nije uključena u cenu.
  = The postage is not included in the price.

• Čak ni poštarina nije uključena u cenu.
  = Not even postage is included in the price.

• U cenu nije uračunata ni poštarina.
  = Even the postage is not included in the price.

These versions are all natural, but they differ slightly in style:

• nije u ceni sounds short and idiomatic
• nije uključena u cenu is a bit more explicit
• nije uračunata u cenu sounds slightly more formal/business-like

The word order is flexible, but this version is natural because it highlights poštarina:

• Čak ni poštarina nije u ceni.

This puts emphasis on the surprising item that is not included.

Other possible orders exist, for example:

• Poštarina čak nije u ceni.
• U ceni nije čak ni poštarina.

But they do not sound exactly the same in emphasis. The original sentence is a very natural way to stress not even the postage.

No. Serbian does not have articles like a and the.

So u ceni can mean:

• in the price
• in a price

In actual usage, context tells you which one is meant. In this sentence, it clearly means in the price or more naturally included in the price.

Yes. That depends on the regional standard:

• cena = Ekavian
• cijena = Ijekavian

So in Croatian, Bosnian, and Montenegrin, or in Serbian Ijekavian usage, you may see:

• Čak ni poštarina nije u cijeni.

That is the same structure, just a different standard pronunciation/spelling.

A straightforward positive version would be:

• Čak je i poštarina u ceni.
  = Even the postage is included in the price.

Or more simply:

• Poštarina je u ceni.
  = Postage is included in the price.

Notice the contrast:

• negative: čak ni ... nije
• positive: čak i ... je

So:

• čak ni poštarina nije... = not even the postage is...
• čak je i poštarina... = even the postage is...