Zanim wyjdę, chcę jeszcze zaparzyć herbatę dla mamy.

This is because wyjdę is from the perfective verb wyjść (to go out / to leave in a completed, one-time sense).

In Polish, perfective verbs do not have a normal present-tense meaning. Their present forms refer to the future.

So:

• wychodzę = I am going out / I go out (imperfective, present)
• wyjdę = I will go out / I leave (perfective, future meaning)

After zanim (before), Polish very often uses this kind of form when talking about a future action:

• Zanim wyjdę... = Before I leave...

They come from two different aspects of the verb:

• wychodzić / wychodzić forms like wychodzę = imperfective
• wyjść / forms like wyjdę = perfective

In this sentence, the speaker means one completed act of leaving, so wyjdę is the natural choice.

Compare:

• Zanim wyjdę... = Before I leave (one future departure)
• Kiedy wychodzę z domu... = When I leave the house / when I am leaving the house (more habitual or ongoing, depending on context)

So wyjdę fits because the sentence is about a single future event.

Because the speaker is expressing a present intention or desire:

• chcę = I want

The meaning is basically: Before I leave, I want to brew some tea for my mum first.

Even though the brewing will happen in the near future, the wanting exists now, so present tense is natural.

Using a future form like będę chciał would usually sound wrong or unnatural here, because it would mean I will want, not I want now.

Because zaparzyć is the perfective form and means to brew / to make as a completed action.

• parzyć = imperfective, focusing on the process or repeated action
• zaparzyć = perfective, focusing on completing the tea-making

In this sentence, the speaker wants to do one complete action before leaving, so zaparzyć is the better choice.

Compare:

• Chcę zaparzyć herbatę. = I want to brew/make some tea.
• Lubię parzyć herbatę. = I like making/brewing tea.

Because herbatę is the accusative singular of herbata.

The verb zaparzyć takes a direct object, and direct objects are usually in the accusative in Polish.

So:

• nominative: herbata
• accusative: herbatę

That is why you say:

• zaparzyć herbatę = to brew tea

not zaparzyć herbata.

Because dla means for, and dla requires the genitive case.

The noun mama changes like this:

• nominative: mama
• genitive: mamy

So:

• dla mamy = for (my) mum

This phrase shows who the tea is for.

Yes. You can also say:

• Zanim wyjdę, chcę jeszcze zaparzyć mamie herbatę.

This uses mamie, the dative form of mama, and it is also very natural.

The difference is small:

• dla mamy emphasizes for my mum
• mamie treats mum more like an indirect object: brew my mum some tea

Both are correct and common. In everyday speech, many speakers might actually prefer zaparzyć mamie herbatę.

Here jeszcze means something like:

• still
• yet
• one more thing before that
• first / before I go

So the sentence suggests the speaker is not quite ready to leave yet, because there is one more action to do first.

In this context, jeszcze often feels very natural and hard to translate with one exact English word. It adds the idea:

• Before I leave, I still want to brew some tea for my mum.
• Before I go, I want to make tea for my mum first.

Because Polish often drops subject pronouns when they are already clear from the verb ending.

Here:

• wyjdę = I will leave
• chcę = I want

The -ę ending already tells you the subject is I.

So adding ja is usually unnecessary unless you want emphasis:

• Ja chcę jeszcze zaparzyć herbatę dla mamy. = I want to brew tea for my mum.
  This sounds more emphatic.

No, Polish word order is fairly flexible, although some versions sound more natural than others.

The original sentence is very natural:

• Zanim wyjdę, chcę jeszcze zaparzyć herbatę dla mamy.

You could also say:

• Chcę jeszcze zaparzyć herbatę dla mamy, zanim wyjdę.
• Jeszcze chcę zaparzyć herbatę dla mamy, zanim wyjdę.

The basic meaning stays the same, but the focus changes slightly.

The original version sounds smooth and neutral because it sets up the time frame first:

• Before I leave...

Because zanim wyjdę is a subordinate clause.

In Polish, subordinate clauses are normally separated by a comma.

So if the zanim clause comes first:

• Zanim wyjdę, chcę jeszcze zaparzyć herbatę dla mamy.

If it comes second:

• Chcę jeszcze zaparzyć herbatę dla mamy, zanim wyjdę.

In both cases, the comma is expected.

No. Even though mamy can sometimes look like mum's when translated loosely, here it is simply the genitive singular after dla.

So:

• dla mamy = for mum
• not mum's

This is a case ending, not a possessive in the English sense.

It can be understood as either, depending on how naturally you would say it in English.

Polish does not have articles like a or the, so herbatę by itself does not tell you that.

In context, it usually means:

• some tea
• a cup of tea
• tea

So zaparzyć herbatę dla mamy is a very natural Polish way to say make/brew tea for mum.