Obwohl ich heute müde bin, höre ich mir noch eine Sprachnachricht von meiner Schwester an und antworte ihr sofort.

Because obwohl is a subordinating conjunction. In German, a subordinate clause introduced by words like obwohl, weil, dass, or wenn sends the conjugated verb to the end of the clause.

So:

• ich bin heute müde = normal main clause word order
• obwohl ich heute müde bin = subordinate clause, so bin moves to the end

In a German main clause, the conjugated verb must be in second position. The whole subordinate clause Obwohl ich heute müde bin counts as position 1, so the verb of the main clause comes immediately after it.

That is why you get:

• Obwohl ich heute müde bin, höre ich ...

and not:

• Obwohl ich heute müde bin, ich höre ...

This is a very common pattern in German:

• Wenn ich Zeit habe, komme ich.
• Obwohl es regnet, gehen wir raus.

Because anhören is a separable verb. In a normal main clause, the prefix separates and goes to the end of the clause.

So:

• infinitive: sich etwas anhören
• main clause: Ich höre mir eine Sprachnachricht an.

This is similar to other separable verbs:

• aufstehen → Ich stehe um 7 Uhr auf.
• einkaufen → Wir kaufen heute ein.

If the verb is in the infinitive or in a subordinate clause, it stays together:

• Ich möchte mir die Nachricht anhören.
• ..., weil ich mir die Nachricht anhöre.

The verb here is really sich etwas anhören, which often means to listen to something or to listen to something all the way through / intentionally. The mir is a dative reflexive pronoun matching ich.

So:

• ich höre mir ... an
• du hörst dir ... an
• er hört sich ... an

In English, this extra pronoun usually is not translated literally. You would normally just say I listen to a voice message.

It is part of the normal pattern of this verb, not a separate word meaning to myself in a strong literal sense.

Because eine Sprachnachricht is the direct object of anhören, so it is in the accusative case.

Here, Sprachnachricht is feminine, and the feminine accusative singular article is eine.

So:

• nominative: eine Sprachnachricht
• accusative: eine Sprachnachricht

For feminine nouns, nominative and accusative often look the same, but grammatically it is still accusative because it is the thing being listened to.

It is dative because the preposition von always takes the dative.

So:

• von meiner Schwester = from my sister

Here, von meiner Schwester describes where the voice message comes from.

Examples:

• eine E-Mail von meinem Lehrer
• ein Geschenk von meiner Freundin

So the pattern is:

• von + dative

Because the verb antworten takes the person in the dative, not the accusative.

So:

• jemandem antworten = to answer someone

That gives:

• Ich antworte ihr. = I answer her / I reply to her.

Not:

• Ich antworte sie.

If you want to mention the thing you are answering, that can also appear:

• Ich antworte ihr auf die Nachricht.
• Ich antworte ihr sofort.

This is a very important verb pattern to learn:

• helfen → jemandem helfen
• danken → jemandem danken
• antworten → jemandem antworten

Here noch means something like still, yet, or one more depending on how you phrase it in English.

In this sentence, it suggests that despite being tired, the speaker will still do this, or will listen to one more message before stopping.

So the feeling is:

• Even though I’m tired today, I’ll still listen to one more voice message...

German noch is very common and has several related uses, for example:

• Ich bin noch hier. = I’m still here.
• Noch einen Kaffee? = Another coffee?
• Ich mache das noch. = I’ll still do that / I haven’t done it yet, but I will.

Sofort is an adverb meaning immediately / right away. In German, adverbs can move around somewhat, but some positions sound more natural than others.

Here:

• ... und antworte ihr sofort

is a very normal placement. The pronoun ihr usually comes quite early, and sofort comes after it.

You could also say:

• ... und antworte sofort ihr

but that sounds less natural in most contexts.

So the sentence uses the most idiomatic order:

• verb
• pronoun object
• adverb

Not in exactly the same structure. Obwohl and trotzdem are related in meaning, but they work differently.

• obwohl = subordinating conjunction, introducing a subordinate clause
• trotzdem = adverb meaning nevertheless / all the same

So you can say:

• Obwohl ich heute müde bin, höre ich mir noch eine Sprachnachricht an.

Or you can rewrite it as:

• Ich bin heute müde, trotzdem höre ich mir noch eine Sprachnachricht an.

Both are correct, but the grammar is different.

Because German very often forms compound nouns by joining words together into one noun.

Here:

• Sprache = language / speech
• Nachricht = message

Together:

• Sprachnachricht = voice message

This is completely normal in German. Other examples:

• Handybildschirm = phone screen
• Kinderbuch = children’s book
• Bahnhofstraße = train station street

The final part usually determines the gender, so because Nachricht is feminine, Sprachnachricht is also feminine: die Sprachnachricht.