Я достала иголку и белую нитку, потому что на куртке около шва появилась дырка.

Because the verb is in the past tense, and in Russian past tense verbs agree with the speaker’s or subject’s gender and number.

• достал = masculine
• достала = feminine
• достало = neuter
• достали = plural

So Я достала tells us the speaker is female. A male speaker would say Я достал.

Because they are the direct objects of достала. In Russian, direct objects often take the accusative case.

Here:

• иголка → иголку
• нитка → нитку

Both are feminine nouns ending in -а, so in the accusative singular they usually change to -у.

So:

• Я достала иголку = I took out a needle
• Я достала нитку = I took out thread

The adjective белую has to agree with нитку in gender, number, and case.

Since нитку is:

• feminine
• singular
• accusative

the adjective must also be feminine singular accusative:

• белая нитка = nominative
• белую нитку = accusative

This is standard adjective-noun agreement in Russian.

Because here на means on in the sense of location, not movement.

Russian uses:

• на + prepositional for location: on / at
• на + accusative for movement toward something

So:

• на куртке = on the jacket
• на куртку = onto the jacket

In this sentence, the hole is already located on the jacket, so Russian uses the prepositional case: на куртке.

Около means near / by, and it requires the genitive case.

So:

• шов = seam
• шва = of the seam / near the seam

After около, Russian uses genitive:

• около дома
• около окна
• около шва

So около шва means near the seam.

Because the subject is дырка, and дырка is a feminine noun.

In the past tense, Russian verbs agree with the subject:

• появился = masculine
• появилась = feminine
• появилось = neuter
• появились = plural

So:

• появилась дырка = a hole appeared

Even though дырка comes after the verb, it is still the subject.

Because it is the subject of появилась.

Russian word order is more flexible than English. The subject does not have to come before the verb.

So both of these are grammatically possible:

• Дырка появилась.
• Появилась дырка.

In both cases, дырка is still the subject and stays in the nominative case.

The version with the verb first often sounds more natural when introducing something new: a hole appeared / there appeared a hole.

Because появилась means appeared / showed up / came into being, which emphasizes that the hole was not there before and then appeared.

Compare:

• На куртке была дырка = There was a hole in the jacket
• На куртке появилась дырка = A hole appeared in the jacket

So появилась gives the idea of a newly formed hole, which fits the context well.

Yes. Потому что is a very common fixed expression meaning because.

It introduces a reason:

• Я ушёл, потому что устал.
• Она открыла окно, потому что было жарко.

In your sentence:

• Я достала иголку и белую нитку, потому что...

= I took out a needle and white thread, because...

Also note the comma before потому что. In Russian, subordinate clauses introduced by потому что are normally separated by a comma.

Yes, often it can be omitted if the subject is clear from context.

Russian frequently drops personal pronouns when they are obvious:

• Достала иголку и белую нитку...

would still be understandable, especially in conversation or in a narrative where we already know who is speaking.

But keeping Я is also perfectly normal. It can make the sentence a bit clearer or slightly more emphatic.

Both relate to thread, but they are used a little differently.

• нить is the more basic or dictionary-style word for thread
• нитка is a common everyday form and often feels very natural when talking about sewing thread

In ordinary speech, especially in practical contexts like sewing, нитка is extremely common.

So белую нитку sounds very natural here.

Because both nouns are direct objects of the same verb достала.

Russian, like English, can list multiple objects after one verb:

• достала иголку и белую нитку
• купил хлеб и молоко
• увидела брата и сестру

There is no need for a preposition here. She simply took out two things:

• a needle
• white thread

Yes, it is natural, and Russian word order can be changed for emphasis.

The given sentence is neutral and natural:

• Я достала иголку и белую нитку, потому что на куртке около шва появилась дырка.

But Russian could also say things like:

• Потому что на куртке около шва появилась дырка, я достала иголку и белую нитку.
• Я достала белую нитку и иголку, потому что...
• На куртке около шва появилась дырка, поэтому я достала иголку и белую нитку.

The basic grammar stays the same, but the emphasis shifts slightly. Russian allows this kind of flexibility much more than English does.