Za doručak jedem jabuku i pijem mleko.

Because Serbian often uses za + accusative to mean for a meal:

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

So Za doručak jedem jabuku i pijem mleko means that this is what the speaker has for breakfast.

Also, doručak is a masculine inanimate noun, and in the singular its accusative form is the same as its nominative form, so it stays doručak.

It is in the accusative because the preposition za normally takes the accusative in this expression.

So even though doručak looks unchanged, it is still accusative:

• nominative: doručak
• accusative: doručak

That is normal for many masculine inanimate nouns in Serbian.

Because jabuku is the direct object of jedem.

In Serbian, direct objects usually go in the accusative case. So:

• nominative: jabuka = apple
• accusative: jabuku = apple, as the thing being eaten

That is why you get jedem jabuku = I eat/am eating an apple.

It is still a direct object, so it is also in the accusative, but mleko is a neuter noun, and many neuter nouns have the same form in nominative and accusative singular.

So:

• nominative: mleko
• accusative: mleko

The case is different in function, but the form happens to be identical.

They are first person singular present tense forms:

• jedem = I eat / I am eating
• pijem = I drink / I am drinking

They come from these infinitives:

• jesti = to eat
• piti = to drink

Like in many Slavic languages, the Serbian present tense can cover both a general/habitual meaning and a current meaning, depending on context.

Serbian often omits the subject pronoun because the verb ending already tells you who the subject is.

• jedem already means I eat
• pijem already means I drink

So ja is not necessary unless you want emphasis or contrast:

• Ja jedem jabuku, a on jede bananu. = I eat an apple, and he eats a banana.

In your sentence, leaving out ja is the most natural neutral option.

It can be either, depending on context.

• habitual: For breakfast, I eat an apple and drink milk.
• right now: I'm eating an apple and drinking milk for breakfast.

Without extra context, many learners will understand it as a general habit, because za doručak often sounds like a routine statement. But Serbian present tense itself does not force only one reading here.

Yes. Serbian word order is fairly flexible.

Your sentence starts with Za doručak to set the topic first: As for breakfast...

Other possible orders include:

• Jedem jabuku i pijem mleko za doručak.
• Za doručak pijem mleko i jedem jabuku.
• Jabuku jedem za doručak, a mleko pijem.

These versions can sound slightly different in emphasis, but your original sentence is very natural and neutral.

This is about aspect.

• jesti, piti = imperfective verbs
• pojesti, popiti = perfective verbs

In a normal present-tense statement about a current or habitual action, Serbian usually uses the imperfective:

• Jedem jabuku.
• Pijem mleko.

The perfective forms focus on completion:

• pojesti = to eat up, to finish eating
• popiti = to drink up, to finish drinking

So pojedem jabuku and popijem mleko would not be the normal neutral choice here.

Because Serbian has no articles.

So jabuku can mean:

• an apple
• the apple

and mleko can mean:

• milk
• the milk

Context tells you which meaning is intended. In this sentence, the most natural English translation is usually an apple and milk, because it sounds like a general breakfast statement.

If Serbian wants to be more specific, it can use demonstratives or other context words, for example:

• tu jabuku = that apple
• ovo mleko = this milk

Both exist, depending on the variety.

• mleko is the Ekavian form
• mlijeko is the Ijekavian form

In Serbia, mleko is very common and standard in Ekavian Serbian. You may also hear mlijeko in Ijekavian varieties. The grammar of the sentence stays the same either way.