Am Wochenende kochen wir oft Linsen, und zum Frühstück gibt es Müsli mit Quark.

Am is the contraction of an dem. With Wochenende, German normally uses an for time expressions, so am Wochenende is the idiomatic way to say on the weekend / at the weekend.

Also, even when it means on weekends in a general sense, German still usually says am Wochenende with the singular noun.

It can mean either, depending on context.

In this sentence, oft makes it clear that the meaning is habitual, so am Wochenende means on weekends or at the weekend in general, not one specific weekend.

German main clauses follow the verb-second rule. That means the finite verb must come in the second position.

So here:

• Am Wochenende = position 1
• kochen = position 2
• wir comes after that

That is why you get Am Wochenende kochen wir oft Linsen.

Adverbs like oft are commonly placed in the middle of the clause, often after the subject and before the object.

So kochen wir oft Linsen is a very natural order:

• verb: kochen
• subject: wir
• adverb: oft
• object: Linsen

Other placements are possible in some contexts, but this is the most neutral and common one here.

German often leaves out the article when talking about food in a general or indefinite way.

So wir kochen oft Linsen means we often cook lentils, not we often cook the lentils.

If you meant specific lentils, you could use an article, for example:

• die Linsen = the lentils

But here the article-free version is the normal choice.

Zum is the contraction of zu dem.

So:

• zu dem Frühstück → zum Frühstück

In this sentence, zum Frühstück means for breakfast or at breakfast.

This is a very common expression in German.

It is dative.

The preposition zu takes the dative case, and Frühstück is a neuter noun:

• das Frühstück
• dative: dem Frühstück

So zu dem Frühstück becomes zum Frühstück.

Es gibt is a very common German expression meaning there is / there are. In the context of meals, it often means we have or there is served.

So:

• Zum Frühstück gibt es Müsli mit Quark
  = For breakfast, there is muesli with quark = more naturally, We have muesli with quark for breakfast

It is a standard, idiomatic way to talk about what is available or served.

It does not refer to a specific noun here. It is a dummy subject, similar to there in English there is / there are.

So es gibt is best learned as a fixed expression meaning there is / there are.

Because es gibt is a fixed singular construction.

The verb agrees with es, not with the noun that comes after it. So German says:

• Es gibt Müsli
• Es gibt Linsen
• Es gibt viele Möglichkeiten

In all of these, the verb stays singular: gibt.

Mit always takes the dative case.

So Quark is in the dative here. The form does not visibly change because there is no article, and the noun itself stays the same in this phrase.

If you included the article, you would see the dative more clearly:

• der Quark
• mit dem Quark

So mit Quark means with quark, and the case is dative.

For the same reason as with Linsen: when talking about food in a general or unspecified amount, German often uses no article.

So es gibt Müsli mit Quark simply means there is muesli with quark or we have muesli with quark.

If you were talking about a specific muesli, you might say das Müsli.

Yes. German word order is flexible, especially with time expressions, but the verb-second rule still applies in main clauses.

For example, this is also correct:

• Wir kochen am Wochenende oft Linsen, und zum Frühstück gibt es Müsli mit Quark.

The difference is mostly about emphasis. Starting with Am Wochenende puts more focus on the time expression.