Сёстры всегда помогают друг другу и редко обижаются друг на друга.

Both spellings are seen, but сёстры is the fully correct spelling because the word is pronounced with ё: сё-стры.

In everyday writing, Russians often replace ё with е, so you may very often see сестры in normal texts. But for a learner, ё is helpful because it shows both the pronunciation and the stress.

• сестра́ = sister
• сёстры = sisters

Notice that the stress changes:

• singular: сестра́
• plural: сёстры

Сёстры is in the nominative plural because it is the subject of the sentence.

The sentence is about what the sisters do:

• Сёстры always help each other...
• Сёстры rarely get offended at each other...

So сёстры answers who? and is therefore nominative.

Помогают is the correct 3rd person plural present tense form of помогать.

Conjugation:

• я помогаю
• ты помогаешь
• он/она помогает
• мы помогаем
• вы помогаете
• они помогают

Since сёстры means they, the verb must be помогают.

Also, Russian verbs do not take an extra ending like -ть in finite forms. -ть is the infinitive ending, as in помогать.

Yes, literally друг другу comes from friend to friend, but in modern Russian it is a fixed expression meaning each other or one another.

So:

• помогают друг другу = help each other

It does not mean that there are actual male friends in the sentence. It is just the normal Russian reciprocal expression.

Russian often expresses each other by combining forms of друг with different cases:

• друг друга
• друг другу
• друг на друга
• друг с другом

The form changes depending on what the verb or preposition requires.

Because the verb помогать takes the dative case.

You help to someone in Russian:

• помогать маме
• помогать брату
• помогать друзьям

So when the meaning is help each other, Russian uses the reciprocal expression in the dative:

• друг другу

That is why:

• Сёстры помогают друг другу.

These are two different verbs in meaning:

• обижать = to offend someone
• обижаться = to be offended, to take offense

So:

• Они обижают друг друга = They offend each other.
• Они обижаются друг на друга = They get offended at each other / They take offense at each other.

In your sentence, the meaning is that the sisters themselves feel offended only rarely, so Russian uses the reflexive form обижаться.

The ending -ся often gives a reflexive or middle meaning, though its exact function depends on the verb.

Because обижаться is used with the preposition на:

• обижаться на брата
• обижаться на подругу
• обижаться на родителей

So if you want to say be offended at each other, Russian keeps that same pattern:

• обижаться друг на друга

Here the reciprocal phrase matches the preposition:

• друг на друга

So the difference is caused by the verb pattern:

• помогать кому? → друг другу
• обижаться на кого? → друг на друга

After на with обижаться, Russian uses the accusative case.

That is why the form is друга:

• обижаться на брата
• обижаться на сестру
• обижаться на друга

In the reciprocal expression:

• друг на друга

the друга part reflects the accusative form required by на in this construction.

Because Russian does not have one single unchanging word for each other.

Instead, it uses forms of друг that change according to grammar:

• друг другу = to each other
• друг друга = each other
• друг на друга = at each other / against each other
• друг с другом = with each other

So the form of each other depends on the verb and any preposition attached to it.

This is very natural in Russian, even though it feels more complicated than English.

There is no comma because this is one sentence with a single subject and two coordinated predicates:

• Сёстры always help each other
• and rarely get offended at each other

The subject сёстры applies to both verbs:

• помогают
• обижаются

So this is a normal compound predicate structure, and no comma is needed before и.

They are adverbs modifying the verbs:

• всегда помогают = always help
• редко обижаются = rarely get offended

This placement is very natural in Russian. Adverbs often come before the verb, especially in neutral word order.

You could move them for emphasis, but the original sentence is the most neutral and standard:

• Сёстры всегда помогают друг другу и редко обижаются друг на друга.

Both are imperfective verbs:

• помогать → помогают
• обижаться → обижаются

The imperfective is used because the sentence describes a general habit or usual behavior, not one completed event.

So the sentence means something like:

• Sisters always help each other and rarely get offended at each other.

This is a typical use of the imperfective in the present tense.

Yes. In natural English, both are usually just translated as each other:

• помогают друг другу = help each other
• обижаются друг на друга = get offended at each other / get upset with each other

English hides the case differences, but Russian shows them clearly. So in translation they may look similar, while in Russian the grammar is different.

Here it means are offended or get offended.

That is an important distinction:

• обижать = to offend someone
• обижаться = to be offended, to take offense

So:

• Сёстры редко обижаются друг на друга does not mean the sisters rarely insult each other directly.
• It means they rarely feel offended by each other.

Depending on context, a smooth English translation could be:

• Sisters always help each other and rarely get offended at each other.
• Sisters always help each other and rarely get upset with each other.

By itself, it most naturally sounds like a general statement about sisters, especially because there is no article in Russian.

So it can mean:

• Sisters always help each other and rarely get offended at each other as a general idea

But in context, it could also refer to some particular sisters if they were already known in the conversation.

Russian does not have a and the, so context decides whether something is general or specific.