Wenn meine Schwester mir eine Sprachnachricht schickt, stummschalte ich sofort das Radio.

Because wenn introduces a subordinate clause. In German, the conjugated verb usually goes to the end of a subordinate clause.

So:

• Wenn meine Schwester mir eine Sprachnachricht schickt
• literally: When my sister to me a voice message sends

This is very normal German word order after conjunctions like:

• wenn = when / if
• weil = because
• dass = that
• ob = whether

So the sentence pattern is:

• Wenn ... schickt, ...

Because the Wenn-clause comes first, and in German the main clause still follows the verb-second rule.

The whole first clause counts as position 1:

• Wenn meine Schwester mir eine Sprachnachricht schickt = position 1
• then the finite verb must come next: stummschalte
• then the subject: ich

So:

• Wenn ..., stummschalte ich ...

If you started with the main clause, you would say:

• Ich stummschalte sofort das Radio, wenn meine Schwester mir eine Sprachnachricht schickt.

Because mir is the dative form of ich, and here it means to me.

In jemandem etwas schicken = to send someone something:

• jemandem = indirect object, dative
• etwas = direct object, accusative

So in the sentence:

• meine Schwester = subject
• mir = to me, indirect object, dative
• eine Sprachnachricht = a voice message, direct object, accusative

Compare:

• Sie schickt mir eine Nachricht. = She sends me a message.
• Sie sieht mich. = She sees me.

So mir is used because the verb schicken often takes a dative recipient.

Because Sprachnachricht is a feminine noun: die Sprachnachricht.

Here it is the direct object of schickt, so it is in the accusative case. For feminine nouns, the accusative article is still eine.

Forms:

• nominative: eine Sprachnachricht
• accusative: eine Sprachnachricht

Since feminine singular does not change here, it looks the same in nominative and accusative.

Because meine Schwester is the subject of the subordinate clause, so it is in the nominative case.

Ask: who is doing the sending?

• meine Schwester is doing it

So it must be nominative.

Forms:

• nominative: meine Schwester
• dative: meiner Schwester

You would use meiner Schwester in a sentence like:

• Ich antworte meiner Schwester. = I reply to my sister.

But here she is the doer of the action, so meine Schwester is correct.

Because Radio is a neuter noun: das Radio.

In this sentence, it is the thing being muted, so it is the direct object of stummschalte and therefore in the accusative case.

For neuter nouns, the definite article is:

• nominative: das
• accusative: das

So the form stays the same:

• das Radio

Sofort means immediately or right away. It is an adverb telling you when the action happens.

So:

• stummschalte ich sofort das Radio
• = I mute the radio immediately

Its position is flexible, but the sentence sounds natural as written. You may also hear:

• Wenn ..., stummschalte ich das Radio sofort.

Both are possible.

Not always. Wenn can mean:

• when for repeated events or general situations
• if for conditions

In this sentence, wenn is best understood as when(ever):

• When my sister sends me a voice message, I immediately mute the radio.

It sounds like a habitual action, something the speaker regularly does.

For a single event in the past, German often uses als instead:

• Als meine Schwester mir eine Sprachnachricht schickte, ...
• = When my sister sent me a voice message, ...
  usually one specific past occasion

Yes, it is understandable and especially natural in modern technical contexts, where stummschalten means to mute.

You will also very commonly hear:

• Ich schalte das Radio stumm.

That is another very natural way to express the same idea.

So for a learner, it is useful to recognize both:

• etwas stummschalten
• etwas stumm schalten / etwas stumm schalten
• etwas stumm schalten or etwas stummstellen may also appear depending on context and style

But in the sentence you were given, stummschalte simply means mute.

A good breakdown is:

• Wenn meine Schwester mir eine Sprachnachricht schickt

  • meine Schwester = subject
  • mir = indirect object, dative
  • eine Sprachnachricht = direct object, accusative
  • schickt = verb

• stummschalte ich sofort das Radio

  • ich = subject
  • stummschalte = verb
  • sofort = adverb
  • das Radio = direct object, accusative

So the full sentence contains two clauses, and each clause has its own structure.

Not very naturally. A very literal version would be:

• When my sister to me a voice message sends, mute I immediately the radio.

That shows the German structure, but it is not good English.

A natural English translation is:

• When my sister sends me a voice message, I immediately mute the radio.

This is a good example of how German and English often use similar words, but different word order.