Do košíku dám nejen mléko, ale i sýr, máslo a jablka.

Because do expresses movement into something, while v / ve usually expresses being in something.

• do košíku = into the basket
• v košíku = in the basket

In this sentence, the speaker is putting things into the basket, so Czech uses do.

Because after the preposition do, Czech uses the genitive case.

The basic form is:

• košík = basket

After do, it becomes:

• do košíku = into the basket

So this is not a random change: it is required by the preposition do.

Dám is the 1st person singular form of dát.

• dát = to give / to put / to place, depending on context
• dám = I will give / I will put

In this sentence, the meaning is I’ll put.

Because dát is a perfective verb, its present-tense form usually has a future meaning:

• dám = I will put not usually I am putting

This is a very common Czech verb pair:

• dát → perfective
• dávat → imperfective

So:

• dám = I’ll put / I’ll give once, as a completed action
• dávám = I am putting, I put, I usually put, depending on context

In this sentence, dám fits because the speaker is talking about a completed action: putting the items into the basket.

They are the direct objects of dám, so they are in the accusative case.

In this sentence:

• mléko = milk
• sýr = cheese
• máslo = butter
• jablka = apples

For some Czech nouns, the accusative looks exactly like the nominative, especially with:

• many inanimate masculine nouns
• many neuter nouns
• many inanimate plural nouns

So although the forms may look unchanged, grammatically they are functioning as accusative objects.

Because here jablka is the accusative plural (same form as nominative plural for this noun), and it is the direct object of the verb.

• jablka = apples
• jablek is a genitive plural form, used in different situations

Examples:

• Koupím jablka. = I’ll buy apples.
• Bez jablek. = without apples.

So in this sentence, jablka is correct because the apples are what the speaker will put into the basket.

This is a fixed Czech pattern meaning:

• not only ... but also ...

So:

• nejen mléko, ale i sýr, máslo a jablka = not only milk, but also cheese, butter, and apples

It is a very common structure.

You may also see similar versions such as:

• nejen ..., ale také ...
• nejen ..., ale i ...

Both are natural.

Because ale means but, and in Czech it is normally separated by a comma in this kind of structure.

So:

• nejen mléko, ale i sýr...

The comma is standard Czech punctuation here.

Yes. In this sentence, i means also / too / even, depending on context.

In the phrase ale i, it helps build the meaning:

• but also

So:

• nejen X, ale i Y = not only X, but also Y

You could also see ale také, which means almost the same thing.

Czech word order is much more flexible than English word order. Starting with Do košíku puts early emphasis on the destination: into the basket.

Compare:

• Do košíku dám nejen mléko...
• Dám do košíku nejen mléko...

Both are possible, but they sound slightly different in focus.

The version with Do košíku first may feel a bit more natural if the basket is already the topic, or if the speaker wants to highlight where the items are going.

Czech does not have articles like a or the.

So košík / košíku can mean:

• a basket
• the basket

The exact meaning comes from context.

In many sentences, English needs an article, but Czech simply does not use one.

Yes. That would still be correct and natural.

For example:

• Do košíku dám nejen mléko, ale i sýr, máslo a jablka.
• Do košíku dám nejen mléko, ale také sýr, máslo a jablka.

Both mean the same thing: I’ll put not only milk, but also cheese, butter, and apples into the basket.

Ale také can sound a little fuller or slightly more formal, while ale i is very common and natural.

Yes, most naturally it is.

Because dám is a perfective verb form, it usually refers to a future completed action:

• Do košíku dám... = I’ll put into the basket...

Even though the form looks like a present tense form, with perfective verbs in Czech it usually has future meaning.

So a learner should usually understand dám here as I will put.