W mojej koszuli jest mała dziura, więc biorę igłę i białą nitkę.

Because the preposition w means in here, and after w (when it means location, not movement), Polish normally uses the locative case.

So:

• moja koszula = my shirt (basic dictionary form, nominative)
• w mojej koszuli = in my shirt (locative)

Both words change:

• moja → mojej
• koszula → koszuli

This is a very common pattern with feminine nouns:

• moja torba → w mojej torbie
• ta szafa → w tej szafie

Here w koszuli is the natural choice, because the hole is understood as being in the fabric.

Compare:

• dziura w koszuli = a hole in the shirt
• plama na koszuli = a stain on the shirt
• guzik na koszuli = a button on the shirt

So w is used for something embedded in or affecting the material itself, while na is used more for something on the surface.

Because mała dziura is the thing that exists/is there, so it stays in the nominative case.

Polish often uses jest the way English uses there is:

• Jest mała dziura. = There is a small hole.

Here:

• mała dziura = nominative

But after a verb like see, you would use the accusative:

• Widzę małą dziurę. = I see a small hole.

So:

• after jest in this kind of existence sentence: mała dziura
• as a direct object: małą dziurę

Because Polish has no articles. There is no direct equivalent of English a/an/the.

So mała dziura can mean:

• a small hole
• the small hole

The context tells you which meaning is intended. In this sentence, English naturally uses a small hole.

Because the verb ending already tells you the subject.

• biorę = I take / I am taking

The ending -ę shows first person singular, so ja is usually unnecessary.

Polish often drops subject pronouns unless they are needed for emphasis or contrast:

• Biorę igłę. = I’m taking a needle.
• Ja biorę igłę, a ty nitkę. = I’m taking the needle, and you’re taking the thread.

In the second example, ja is used for emphasis/contrast.

This is about aspect.

• brać / biorę = imperfective
• wziąć / wezmę = perfective

In this sentence, biorę sounds like I’m taking or I take as part of what is happening right now in the situation.

So the sentence feels like a present-time description:

• There’s a hole, so I take / I’m taking a needle and white thread.

If you said wezmę, it would sound more like:

• I’ll take a needle and white thread.

That is also possible in some contexts, but it shifts the meaning slightly toward a single completed future action rather than present narration.

Because they are the direct objects of biorę, so they go into the accusative case.

Dictionary forms:

• igła = needle
• nitka = thread

After biorę:

• biorę igłę
• biorę nitkę

For many feminine nouns ending in -a, the accusative singular changes to -ę:

• książka → książkę
• kawa → kawę
• nitka → nitkę

Because the adjective has to match the noun in case, gender, and number.

The basic form is:

• biała nitka = white thread (nominative)

But in the sentence, nitkę is accusative, so the adjective also changes:

• białą nitkę = white thread (accusative)

So:

• biała matches nitka
• białą matches nitkę

This agreement is a central feature of Polish grammar.

They are related, but they do different jobs:

• więc = so / therefore
  introduces a result
• bo = because
  introduces a reason

Your sentence is structured as:

• There is a hole, so I take a needle and white thread.

That is why więc fits:

• W mojej koszuli jest mała dziura, więc biorę igłę i białą nitkę.

You could also say:

• Biorę igłę i białą nitkę, bo w mojej koszuli jest mała dziura.

That means:

• I’m taking a needle and white thread because there is a small hole in my shirt.

So both are possible, but the sentence structure changes.

Because więc is a coordinating conjunction, and in Polish it is normally preceded by a comma when it joins two clauses.

So:

• W mojej koszuli jest mała dziura, więc biorę igłę i białą nitkę.

This is standard Polish punctuation.

Yes. Polish word order is more flexible than English word order, because the cases show what each word is doing.

Your sentence has a very natural neutral order:

• W mojej koszuli jest mała dziura, więc biorę igłę i białą nitkę.

But other orders are possible, for example:

• Biorę więc igłę i białą nitkę.
• Igłę i białą nitkę biorę, bo w mojej koszuli jest mała dziura.

These alternatives may sound more emphatic, literary, or context-dependent. The original version is a good standard choice for learners.