Meine Schwester bringt ein veganes Mittagessen mit, während ich nur einen Joghurt mit Blaubeeren esse.

Because mitbringen is a separable verb. In a main clause, the conjugated part goes in the usual verb position, and the prefix moves to the end:

• mitbringen = to bring along / bring with you
• Meine Schwester bringt ein veganes Mittagessen mit.

So:

• bringt = the conjugated verb
• mit = the separated prefix

In an infinitive or participle, it stays together:

• Sie will ein Mittagessen mitbringen.
• Sie hat ein Mittagessen mitgebracht.

Because während introduces a subordinate clause here. In German subordinate clauses, the conjugated verb usually goes to the end.

So:

• während ich nur einen Joghurt mit Blaubeeren esse

Compare:

• Main clause: Ich esse einen Joghurt.
• Subordinate clause: ..., während ich einen Joghurt esse.

That final verb position is one of the most important word-order patterns in German.

Here, während means while.

It connects two actions happening at the same time, or it can sometimes suggest a contrast:

• Meine Schwester bringt ... mit, während ich ... esse.
• My sister brings a vegan lunch, while I only eat a yogurt with blueberries.

Be careful: während can also be a preposition meaning during, but that is a different use:

• während des Essens = during the meal

In your sentence, it is a conjunction, not a preposition.

Because während ich nur einen Joghurt mit Blaubeeren esse is a subordinate clause, and German normally separates subordinate clauses with a comma.

So the comma is required here:

• Meine Schwester bringt ein veganes Mittagessen mit, während ich ... esse.

This is very standard in written German.

Because Joghurt is treated as masculine here: der Joghurt.

It is the direct object of esse, so it must be in the accusative case. For a masculine noun, ein changes to einen in the accusative:

• Nominative: ein Joghurt
• Accusative: einen Joghurt

So:

• Ich esse einen Joghurt.

That is a very common German pattern:

• Ich habe einen Hund.
• Sie kauft einen Apfel.

Because Mittagessen is neuter: das Mittagessen.

After the indefinite article ein, an adjective before a neuter noun in the nominative or accusative singular usually takes -es:

• ein veganes Mittagessen

So the structure is:

• ein = indefinite article
• veganes = adjective with the correct ending
• Mittagessen = noun

Compare:

• ein gutes Buch
• ein kleines Kind
• ein veganes Mittagessen

Because Mittagessen is neuter, and the indefinite article ein looks the same in both nominative and accusative.

So:

• Nominative: ein veganes Mittagessen
• Accusative: ein veganes Mittagessen

The form does not change, even though the function in the sentence may be different.

In this sentence, it is the object of bringt mit, so it is accusative.

Nur means only.

It adds the idea that the speaker is eating just a yogurt with blueberries, possibly in contrast to the sister bringing a full vegan lunch.

• während ich nur einen Joghurt mit Blaubeeren esse
• while I only eat a yogurt with blueberries

Its placement before einen Joghurt makes it sound like the only thing being eaten is that yogurt.

No. They are two different things.

1. In bringt ... mit, the mit is the prefix of the separable verb mitbringen.

   • mitbringen = to bring along

2. In mit Blaubeeren, mit is a normal preposition meaning with.

   • ein Joghurt mit Blaubeeren = a yogurt with blueberries

So even though both are spelled mit, they have different grammatical roles in the sentence.

Because German often uses no article when talking about ingredients or contents in a general way.

So:

• Joghurt mit Blaubeeren = yogurt with blueberries
• Brot mit Butter = bread with butter
• Reis mit Gemüse = rice with vegetables

If you said mit den Blaubeeren, it would sound more like you mean some specific blueberries already known from the context.

Also, mit takes the dative case, but because there is no article here, you do not see a visible article change.

In German, all nouns are capitalized, so Schwester must begin with a capital letter.

• meine = possessive determiner, not capitalized here
• Schwester = noun, so capitalized

This is a basic but very important rule in German spelling.

The first clause follows normal main-clause word order, where the conjugated verb is in second position:

• Meine Schwester = first element
• bringt = conjugated verb in second position
• ein veganes Mittagessen = object
• mit = separated prefix at the end

So the pattern is roughly:

• Subject + verb + object + separable prefix

That is why you get:

• Meine Schwester bringt ein veganes Mittagessen mit.

Yes. German allows that very naturally:

• Während ich nur einen Joghurt mit Blaubeeren esse, bringt meine Schwester ein veganes Mittagessen mit.

If the subordinate clause comes first, the main clause still follows the normal rule that the conjugated verb is in second position:

• first position = the whole subordinate clause
• second position = bringt

So you do not say:

• Während ich ... esse, meine Schwester bringt ... ❌

You say:

• Während ich ... esse, bringt meine Schwester ... ✔️

It mainly expresses simultaneous time: one thing happens while another happens.

But in real usage, it can also carry a slight sense of contrast, especially in sentences like this one:

• My sister brings a vegan lunch, while I only eat a yogurt...

So the sentence can feel like both:

• at the same time
• in contrast

That double effect is very common with während.

Esse is the 1st person singular conjugated form of essen:

• essen = infinitive, to eat
• ich esse = I eat / I am eating

Here the subject is ich, so the verb must be:

• ich esse

Other forms include:

• du isst
• er/sie/es isst
• wir essen
• ihr esst
• sie/Sie essen

Both direct objects are in the accusative case:

• ein veganes Mittagessen — object of mitbringen
• einen Joghurt — object of essen

The prepositional phrase:

• mit Blaubeeren

is not an accusative object. It is a phrase with the preposition mit, which normally takes the dative.

So the sentence contains:

• two accusative direct objects
• one prepositional phrase with mit