Hon och hennes syster blev överens till slut och lovade att inte bråka igen.

Because hennes is the ordinary possessive her, while sin/sitt/sina is the reflexive possessive, used when something belongs to the subject and it appears later in the clause.

In this sentence, hennes syster is part of the subject itself: Hon och hennes syster. Swedish normally does not use sin inside the subject phrase like that.

Compare:

• Hon älskar sin syster = She loves her own sister.
• Hon och hennes syster = She and her sister.

So hennes is the natural choice here.

Blev is the past tense of bli, meaning become, and överens means in agreement / agreed.

So grammatically, blev överens is literally something like became in agreement. In natural English, that usually comes out as agreed, made up, or reached an understanding, depending on context.

It is a very common Swedish way to express that people stopped disagreeing and ended up agreeing.

Because blev focuses on a change: they were not in agreement before, and then they became in agreement.

If you used var överens, that would describe a state: they were in agreement.
But blev överens means they came to an agreement or ended up agreeing.

So the choice of blev fits the idea that something changed.

Yes, överens is usually treated as a predicate adjective, but it behaves like a fixed form.

Many Swedish adjectives change depending on gender, number, or definiteness, but överens does not. It stays överens no matter who is agreeing:

• Jag är överens
• Hon är överens
• De är överens

So even with two people, it still remains överens.

Yes, but the difference is small, and both can often be translated similarly.

• kom överens is very common for reached an agreement / got along / agreed
• blev överens also means that they ended up agreeing, with a bit more focus on the resulting change of state

In many everyday contexts, they are very close. A learner should recognize both.

Till slut means in the end, eventually, or at last.

It tells you that this did not happen immediately. They probably had some conflict first, and only after some time did they become reconciled or agree.

It is an adverbial expression of time/result.

Because Swedish, like English, can use one subject for two coordinated verbs.

Here, the subject is Hon och hennes syster, and it applies to both verbs:

• blev överens
• lovade att inte bråka igen

So the sentence means that she and her sister both became reconciled and both promised not to argue again.

You could repeat the subject, but it would usually sound unnecessary.

These two word orders mean different things.

• lovade att inte bråka = promised not to argue
• lovade inte att bråka = did not promise to argue / did not make that promise

In the sentence you gave, the negation belongs to bråka, not to lovade. So the meaning is that they made a promise, and the content of that promise was not to argue.

That is why the negation comes inside the infinitive clause: att inte bråka.

Because in Swedish infinitive clauses, inte normally comes before the infinitive verb.

So:

• att inte bråka
• att inte gå
• att inte säga något

This is the normal pattern: att + inte + infinitive.

Because Swedish verbs do not change form according to person or number the way English sometimes does.

The past tense form is the same whether the subject is I, she, or they:

• jag lovade
• hon lovade
• de lovade

So even though Hon och hennes syster is plural in meaning, the verb form stays exactly the same.

Igen means again.

In this sentence, it tells us that the arguing happened before, and they are promising not to let it happen one more time.

So inte bråka igen means not argue again.

Yes. Bråka can be used on its own to mean argue, quarrel, or sometimes fight.

If you want to mention the topic, you can add om:

• De bråkade om pengar = They argued about money.

But if the topic does not matter, just bråka is completely normal.

Yes.

Since the subject is Hon och hennes syster, both verbs apply to both people. So the sentence naturally means that the two of them became reconciled and the two of them promised not to argue again.

If you wanted to say that only one of them made the promise, Swedish would normally make that more explicit.