У этой куртки сломалась застёжка, и из-за неё я чуть не опоздала.

Because Russian often uses у + genitive to talk about possession or something belonging to/associated with something.

So У этой куртки сломалась застёжка literally means something like:

• At this jacket, the fastening broke
• more naturally: This jacket’s fastening broke / The fastening on this jacket broke

This is a very common Russian pattern, especially when talking about parts of things:

• У машины сломалось колесо = The car’s wheel broke
• У меня болит голова = My head hurts

So у этой куртки is not the subject; it sets up which jacket we are talking about.

Because у requires the genitive case.

The dictionary form is эта куртка, but after у it becomes:

• этой = genitive singular feminine of эта
• куртки = genitive singular of куртка

The adjective/demonstrative must agree with the noun in case, gender, and number, so both change together:

• nominative: эта куртка
• genitive: этой куртки

Because the grammatical subject is застёжка, and застёжка is feminine singular.

In Russian past tense, the verb agrees with the subject in gender and number:

• сломался = masculine
• сломалась = feminine
• сломалось = neuter
• сломались = plural

So:

• застёжка сломалась
• замок сломался
• колёса сломались

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

Because сломалась is from сломаться, which means to break / become broken.

Compare:

• сломать = to break something
• сломаться = to break, to get broken

So:

• Я сломала застёжку = I broke the fastening
• Застёжка сломалась = The fastening broke

The -ся form is very common when something happens to the object itself without naming an external doer.

Застёжка is a general word for a fastening or closure on clothing.

Depending on context, it might refer to:

• a zipper
• a clasp
• a snap
• a fastening mechanism in general

So in this sentence, it does not necessarily tell you the exact type of closure. It just means the thing used to fasten the jacket.

Here из-за means because of, and it takes the genitive case.

The pronoun она changes like this:

• nominative: она
• genitive: её / неё

After a preposition, Russian usually uses the form with н-, so:

• из-за неё = because of her / it

So the structure is:

• из-за + genitive

Examples:

• из-за дождя = because of the rain
• из-за неё = because of her / it

Grammatically, it could refer to either one, because both are feminine singular:

• куртка
• застёжка

But in context, most learners will understand it as referring to the thing that caused the problem — most likely the fastening.

Still, there is some potential ambiguity. If a speaker wanted to make it fully clear, they could say:

• из-за сломанной застёжки я чуть не опоздала
• из-за этой куртки я чуть не опоздала

So yes, неё is a little ambiguous on its own, even though the intended meaning is usually clear from context.

Чуть не means almost or came close to doing something.

So:

• я чуть не опоздала = I almost was late / I almost ended up being late

An important point: this usually means the thing did not actually happen.

So the speaker is saying she was not late, but she came very close.

Other examples:

• Я чуть не упал = I almost fell
• Она чуть не заплакала = She almost cried

Because the speaker is female.

In Russian past tense, verbs agree with the speaker’s gender when the subject is I in the past:

• я опоздал = said by a man
• я опоздала = said by a woman

So this sentence tells us the speaker is female.

Yes, it is natural. Russian word order is flexible, and different orders shift the emphasis.

The given sentence:

• У этой куртки сломалась застёжка

puts this jacket first as the topic.

You could also say:

• Застёжка у этой куртки сломалась

This puts a bit more focus on the fastening.

Both are normal. The version you have sounds very natural in everyday Russian.

Yes, but Russian usually prefers the у + genitive pattern here.

English often says:

• this jacket’s fastening
• the fastening on this jacket

Russian more naturally says:

• у этой куртки застёжка...
• or застёжка у этой куртки...

A direct possessive structure is much less central in Russian than in English, especially for body parts, parts of objects, and things associated with someone/something.