Zum Frühstück esse ich ein Rührei mit Brot.

Yes. Zum Frühstück is the usual German way to say for breakfast or at breakfast in this kind of sentence.

• zum = zu dem
• Frühstück = breakfast

So literally, zum Frühstück is something like at the breakfast meal, but in natural English we usually translate it as for breakfast.

This is a very common fixed expression:

• zum Frühstück = for breakfast
• zum Mittagessen = for lunch
• zum Abendessen = for dinner

German uses zu here, not a direct equivalent of English for.

Because Frühstück is a noun, and all nouns are capitalized in German.

So in this sentence:

• Frühstück = noun
• Rührei = noun
• Brot = noun

That is why all three begin with capital letters.

This is because German main clauses usually follow the verb-second rule.

In a normal statement, the finite verb goes in the second position. The first position can be taken by different kinds of elements, not just the subject.

Here, the first element is:

• Zum Frühstück

So the verb must come next:

• Zum Frühstück esse ich ein Rührei mit Brot.

Structure:

• 1st position: Zum Frühstück
• 2nd position: esse
• then the subject: ich

If you start with the subject instead, then you get:

• Ich esse zum Frühstück ein Rührei mit Brot.

That is also correct.

Yes, absolutely.

Both are correct:

• Zum Frühstück esse ich ein Rührei mit Brot.
• Ich esse zum Frühstück ein Rührei mit Brot.

The difference is mainly focus:

• Zum Frühstück ... puts more emphasis on when / for which meal
• Ich ... starts more neutrally with the subject

This kind of word order change is very common in German.

Rührei is neuter:

• das Rührei

So in the accusative singular, the indefinite article is:

• ein Rührei

That is because neuter ein looks the same in nominative and accusative:

• nominative: ein Rührei
• accusative: ein Rührei

Here it is accusative because it is the direct object of essen.

Good question. The difference is about how German treats these nouns in this sentence.

• ein Rührei = one serving/portion of scrambled eggs
• Brot = bread in a general sense, as an accompaniment

So:

• ein Rührei sounds like a specific countable item on the plate
• mit Brot means with bread in a general, non-specific way

This is similar to English:

• I eat an omelet with bread not necessarily
• with a bread

You could add an article if you wanted to make it more specific:

• mit dem Brot = with the bread
• mit einem Brot = with a loaf/roll of bread, depending on context

But mit Brot is the natural generic phrasing here.

It is in the accusative case because it is the direct object of essen.

The verb essen usually takes something you eat as a direct object:

• Ich esse einen Apfel.
• Ich esse ein Rührei.

In this sentence:

• ich = subject
• esse = verb
• ein Rührei = direct object, so accusative

Because Rührei is neuter, the article ein does not change form here.

After mit, German always uses the dative case.

So mit Brot is dative.

The reason you do not see a special ending here is that:

• there is no article
• the noun Brot often looks the same in several cases

Compare:

• nominative: das Brot
• accusative: das Brot
• dative: dem Brot

Without an article, just Brot stays the same in form here, but grammatically it is still understood as dative because mit requires dative.

Because zum is the normal contraction of zu dem.

• zu dem → zum

German very often contracts certain preposition + article combinations:

• zu dem → zum
• zu der → zur
• in dem → im
• an dem → am

So zum Frühstück is just the standard contracted form. Using zu dem Frühstück here would sound unnatural.

It is singular here.

• ein Rührei = one scrambled-egg dish / one portion of scrambled eggs

Even though scrambled eggs are made from multiple eggs, German often treats Rührei as a single dish.

So it works like:

• ein Rührei
• das Rührei

If you wanted plural, that would usually refer to multiple portions:

• zwei Rühreier

But in everyday use, the singular is much more natural in a sentence like this.

Normally, no. In this context, mit Brot is understood as served/eaten with bread, not physically mixed together.

That is a very common use of mit in food descriptions:

• Fisch mit Reis = fish with rice
• Suppe mit Brot = soup with bread
• Rührei mit Brot = scrambled eggs with bread

So the meaning is accompaniment, not mixture.