V košíku nemám ani dopis, ani známku, jen rohlíky a máslo.

Because the preposition v means in here, and when it expresses location, it requires the locative case.

• basic form: košík = basket
• after v for location: v košíku = in the basket

So košíku is the locative singular form of košík.

Czech word order is more flexible than English word order. Starting with V košíku puts the location first and sets the scene: As for the basket...

A more neutral order could also be:

Nemám v košíku ani dopis, ani známku, jen rohlíky a máslo.

Both are correct, but V košíku at the start gives a slight emphasis to where these things are or are not.

Because Czech often leaves out subject pronouns when they are already clear from the verb form.

• mám = I have
• nemám = I do not have

The ending -m already shows that the subject is I, so já is unnecessary unless you want extra emphasis:

Já nemám... = I don’t have... with emphasis on I

Ani ... ani ... means neither ... nor ... in a negative sentence.

So:

nemám ani dopis, ani známku
= I have neither a letter nor a stamp

A useful extra point: a single ani can also mean not even.

• Nemám ani dopis. = I don’t even have a letter.

But when repeated as ani ... ani ..., it gives the neither ... nor ... meaning.

In Czech, this is normal. Czech commonly allows and expects negative concord, where the verb is negative and other negative-type words appear with it.

So:

Nemám ani dopis, ani známku.

is the normal Czech way to say it.

You would not normally say Mám ani dopis, ani známku with this meaning.

Both nouns are direct objects of mít / nemít, so both are in the accusative case. The reason they look different is that different noun types form the accusative differently.

• dopis is a masculine inanimate noun

  • nominative: dopis
  • accusative: dopis
    So there is no visible change.

• známka is a feminine noun

  • nominative: známka
  • accusative: známku
    So the ending changes to -u.

This is very common in Czech.

Because they are still the things the speaker has, so they are also direct objects of mít and stay in the accusative.

• rohlíky = accusative plural of rohlík
• máslo = accusative singular of máslo

The word jen means only, but it does not change the fact that these nouns are objects of the verb.

So:

jen rohlíky a máslo
= only rolls and butter

That is a very good question. Older Czech, and sometimes more literary or special usages, can use the genitive after negation. But in modern everyday Czech, with nouns like these, the accusative is the normal choice.

So in ordinary modern Czech, you would expect:

• nemám dopis
• nemám známku

not genitive forms here.

For a learner, the safest rule is: in sentences like this, use the accusative after nemám.

Here jen means only or just:

jen rohlíky a máslo
= only rolls and butter

Yes, you could also say pouze, which is slightly more formal or bookish:

V košíku nemám ani dopis, ani známku, pouze rohlíky a máslo.

In everyday speech, jen is very common and natural.

Because Czech does not have articles like English a/an and the.

So Czech simply says:

• v košíku = in a basket / in the basket / in my basket, depending on context
• dopis = a letter / the letter, depending on context

If Czech wants to make my explicit, it can:

v mém košíku = in my basket

But in your sentence, that information is left to context.

The commas help separate the parts clearly.

• ani dopis, ani známku uses a repeated pair: ani ... ani ...
• then jen rohlíky a máslo is added as a contrasting clarification: only rolls and butter

So the commas make the structure easier to read.

A useful nuance: you do not always need a comma before jen in every sentence. For example:

Mám jen rohlíky a máslo.

has no comma. In your sentence, the comma fits because jen rohlíky a máslo comes after the earlier negative list as a kind of contrastive add-on.

A rohlík is a very common Czech bread roll, usually longish and slightly crescent-shaped. In English it is often translated simply as roll or bread roll.

So:

• rohlík = one bread roll
• rohlíky = bread rolls

It is a very everyday Czech food word, so you will see it often.