In meine Brotdose packe ich heute Brot, Käse und einen Apfel.

German often moves a different element to the beginning of the sentence to set the topic or emphasis.

So instead of the more neutral:

Ich packe heute Brot, Käse und einen Apfel in meine Brotdose.

you can also say:

In meine Brotdose packe ich heute Brot, Käse und einen Apfel.

This puts extra focus on what is going into my lunchbox. In English, we might do something similar with stress, but in German word order does a lot of that work.

Because German main clauses follow the verb-second rule.

That means:

• the finite verb must be in the second position
• whatever comes first can be the subject, an object, a time expression, a prepositional phrase, etc.

In this sentence, In meine Brotdose is in first position, so the verb must come next:

• In meine Brotdose = position 1
• packe = position 2
• ich = then comes after the verb

So packe ich is correct here.

Because in here expresses direction/movement into something, so it takes the accusative case.

You are putting food into the lunchbox, not describing where it already is.

• in meine Brotdose = into my lunchbox → accusative
• in meiner Brotdose = in my lunchbox / inside my lunchbox → dative, usually for location

So the contrast is:

• Ich packe das Brot in meine Brotdose. = I put the bread into my lunchbox.
• Das Brot ist in meiner Brotdose. = The bread is in my lunchbox.

In is a two-way preposition in German. That means it can take either:

• accusative for direction/change of location
• dative for location/static position

Here, the action is moving things into the lunchbox, so it is directional:

• in meine Brotdose → accusative

If the sentence described where the items already are, you would use dative:

• In meiner Brotdose sind Brot und Käse.

Because Brot and Käse are being used as uncountable food nouns here, in a general sense:

• Brot = bread
• Käse = cheese

German often leaves out the article when talking about food or substances in a general, non-specific way.

But Apfel is a countable individual item, and here it means an apple, so it takes an article:

• einen Apfel

Compare:

• Ich esse Brot. = I eat bread.
• Ich esse einen Apfel. = I eat an apple.

You could also say ein Brot in some contexts, but that usually means a loaf of bread or a specific bread item, which is not the most natural meaning here.

Because Apfel is:

• masculine: der Apfel
• the direct object here
• therefore in the accusative

The masculine indefinite article changes like this:

• nominative: ein Apfel
• accusative: einen Apfel

So:

• Ein Apfel ist auf dem Tisch. = An apple is on the table.
• Ich packe einen Apfel ein. = I pack an apple.

They are all direct objects, so they are in the accusative.

In this sentence, the thing being packed is:

• Brot
• Käse
• einen Apfel

For Brot and Käse, you do not see a visible case change because:

• das Brot stays das Brot
• der Käse often appears without an article here anyway

But for Apfel, the article shows the accusative clearly:

• ein Apfel → einen Apfel

Brotdose is a very common German word for a lunchbox or food container, especially one used for school or work snacks.

It is a compound noun:

• Brot = bread
• Dose = container, tin, box

So literally it is something like bread box/container, but in everyday German it usually means lunchbox.

Like most German compounds, the gender comes from the last part:

• die Dose
• therefore die Brotdose

So:

• nominative: meine Brotdose
• accusative: meine Brotdose
• dative: meiner Brotdose

Yes, heute can move. German time expressions are fairly flexible, although some positions sound more natural than others.

Your sentence has:

In meine Brotdose packe ich heute Brot, Käse und einen Apfel.

You could also say:

• Ich packe heute Brot, Käse und einen Apfel in meine Brotdose.
• Heute packe ich Brot, Käse und einen Apfel in meine Brotdose.
• Ich packe Brot, Käse und einen Apfel heute in meine Brotdose.
  (possible, though often a bit less natural depending on context)

The version with heute in the middle sounds very normal.

It is natural German.

A native speaker could absolutely say:

In meine Brotdose packe ich heute Brot, Käse und einen Apfel.

It sounds slightly more focused or deliberate than the neutral version starting with Ich, because the lunchbox is placed first for emphasis. But it is not strange or artificial.

A more neutral everyday version would be:

Ich packe heute Brot, Käse und einen Apfel in meine Brotdose.

Both are correct.

Yes, that is also very natural.

That version adds mir, which is a dative pronoun often used when someone is doing something for themselves:

• Ich packe mir heute Brot, Käse und einen Apfel in die Brotdose.

This has a slightly everyday, conversational feel, something like:

• I’m packing myself some bread, cheese, and an apple into my lunchbox today.

Also note:

• in die Brotdose = into the lunchbox
• if it is clear whose lunchbox it is, German often uses the article instead of a possessive

So both of these are natural:

• ... in meine Brotdose
• ... in die Brotdose

The most neutral version is:

Ich packe heute Brot, Käse und einen Apfel in meine Brotdose.

That follows a very common German pattern:

Subject + verb + time + objects + place/direction

Your original sentence is a rearranged version for emphasis:

In meine Brotdose + packe + ich + heute + Brot, Käse und einen Apfel

Both are grammatical; the difference is mainly one of emphasis and information structure.