Während der Tee zieht, bringe ich den Müll raus und mache den Herd aus.

Because während introduces a subordinate clause here.

In German subordinate clauses, the conjugated verb goes to the end:

• Während der Tee zieht
• literally: while the tea steeping-is

That is why you do not say Während der Tee zieht ich... or put zieht earlier.

Because the sentence starts with the subordinate clause:

• Während der Tee zieht, ...

That whole clause takes the first position in the sentence. In German main clauses, the conjugated verb must come second, so after that opening clause you get:

• bringe ich den Müll raus

This is normal German word order:

• Während der Tee zieht, bringe ich den Müll raus.
• Ich bringe den Müll raus, während der Tee zieht.

Both are correct, but the word order changes depending on what comes first.

Here während means while.

It introduces an action happening at the same time as the main action:

• Während der Tee zieht = while the tea is steeping

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

• während des Films = during the film
• Während der Tee zieht = while the tea is steeping

So in your sentence, it is a conjunction, not a preposition.

It often does mean to pull, but like many German verbs, it has several meanings depending on context.

With tea, ziehen means to steep or to brew:

• Der Tee zieht. = The tea is steeping.

This is a very common expression in German. You will also see it with things like:

• den Tee ziehen lassen = to let the tea steep

So this is an idiomatic use, not the basic pull meaning.

This is about case.

• der Tee is the subject of the subordinate clause, so it is in the nominative case.
• den Müll and den Herd are direct objects in the main clause, so they are in the accusative case.

So:

• der Tee = nominative masculine
• den Müll = accusative masculine
• den Herd = accusative masculine

That is why the article changes from der to den.

Because the verb is rausbringen, which is a separable verb.

In a normal main clause, the conjugated part goes in the usual verb position, and the prefix moves to the end:

• Ich bringe den Müll raus.

So:

• full verb: rausbringen
• split form: bringe ... raus

This is very common in German with separable verbs.

It means to take the trash out.

Literally, rausbringen is something like bring out, but in this context the natural English meaning is:

• to take out the trash
• to put the garbage outside

So Ich bringe den Müll raus is a standard everyday phrase.

For the same reason: ausmachen is also a separable verb.

• infinitive: ausmachen
• main clause: Ich mache den Herd aus.

Here ausmachen means to turn off:

• den Herd ausmachen = to turn off the stove

So the sentence contains two separable verbs:

• rausbringen → bringe ... raus
• ausmachen → mache ... aus

No. Ausmachen has several meanings.

Some common ones are:

• to turn off
  
  • das Licht ausmachen = to turn off the light
• to make up / constitute
  
  • Das macht keinen großen Unterschied aus.
• to arrange / agree on
  
  • Wir machen einen Termin aus.

In your sentence, because the object is den Herd, the meaning is clearly to turn off.

Because German uses a comma to separate a subordinate clause from a main clause.

So this comma is required:

• Während der Tee zieht, bringe ich den Müll raus ...

In German, commas with subordinate clauses are much more strictly required than in English.

Because both verbs belong to the same subject: ich.

The structure is:

• bringe ich den Müll raus
• und mache den Herd aus

In English, this works the same way:

• I take out the trash and turn off the stove.

You do not need to repeat the subject unless you want emphasis or clarity.

No, that is not correct standard German.

After the opening subordinate clause, the main clause still follows the verb-second rule, so you need:

• Während der Tee zieht, bringe ich den Müll raus ...

Not:

• Während der Tee zieht, ich bringe ...

This is one of the most important German word-order patterns to learn.

Yes. Raus is a shorter, more conversational form of heraus.

So these are both possible:

• Ich bringe den Müll raus.
• Ich bringe den Müll heraus.

In everyday speech, raus is extremely common. Heraus can sound a little more formal or more explicit, depending on context.

Yes. German often uses the present tense for everyday actions happening now or around now.

In this sentence, the idea is:

• while the tea is steeping,
• I take out the trash
• and turn off the stove

These actions are all presented as part of the current situation, so the present tense is natural.

German does not need a special progressive form like English is steeping or am taking out here.

Yes. You can say:

• Ich bringe den Müll raus und mache den Herd aus, während der Tee zieht.

That means the same thing overall. The difference is mainly focus:

• Während der Tee zieht, ... emphasizes the time setting first.
• Ich bringe den Müll raus ..., während der Tee zieht. starts with what I am doing.

Both are natural.