Сестри довіряють одна одній і рідко сперечаються.

Сестри is the nominative plural of сестра (sister).

It is used because сестри is the subject of the sentence: the sisters are the ones doing the actions.

• singular: сестра
• plural: сестри

So:

• Сестра довіряє... = The sister trusts...
• Сестри довіряють... = The sisters trust...

Довіряють is the 3rd person plural present tense form of довіряти.

That means it matches сестри:

• я довіряю = I trust
• ти довіряєш = you trust
• вона довіряє = she trusts
• вони довіряють = they trust

Since сестри is plural, the verb is plural too: довіряють.

Because довіряти takes the dative case, not the accusative.

In English, we say trust someone.
In Ukrainian, the grammar is closer to trust to someone.

So:

• довіряти сестрі = to trust the sister
• довіряти друзям = to trust friends
• довіряти одна одній = to trust each other

That is why the second word in the pair is одній, a dative form.

Одна одній is the feminine version of each other.

It is built from forms of one:

• одна = feminine one
• одній = feminine dative to one

Literally, it is something like one to another, but in natural English it means each other.

Because the subject is сестри (female people), the feminine forms are used:

• сестри довіряють одна одній
• подруги допомагають одна одній

That is normal. In Ukrainian, reciprocal expressions like одна одній use singular forms, even though the overall meaning is plural.

The idea is:

• one sister trusts the other
• and the other trusts the first

So the phrase is conceptually one ... the other one, not a plural noun phrase.

This is why you get:

• брати допомагають один одному
• сестри довіряють одна одній

Not in this sentence if you want standard, natural Ukrainian.

Because сестри refers to females, the usual form is:

• одна одній

Compare:

• брати допомагають один одному = brothers help each other
• сестри допомагають одна одній = sisters help each other

So один одному is masculine, while одна одній is feminine.

Because the verb is сперечатися, which is the normal dictionary form meaning to argue / to dispute.

The -ся here is part of the verb. It often gives a reflexive or reciprocal sense, and with this verb it fits the idea of people arguing with each other.

So:

• сперечатися = to argue
• сперечаються = they argue

In this sentence, it does not mean they argue with themselves. It simply means they argue.

Both verbs are present tense and imperfective:

• довіряють
• сперечаються

Here the present tense expresses a general/habitual fact, not necessarily something happening right this second.

So the sentence means something like:

• they trust each other
• they rarely argue

as a regular pattern or characteristic.

Рідко is an adverb meaning rarely, and placing it before the verb is very natural in Ukrainian.

So:

• рідко сперечаються = rarely argue

Ukrainian word order is fairly flexible, but this placement is standard and neutral.

You may also hear other orders for emphasis, but рідко сперечаються is the most straightforward here.

Because Ukrainian often leaves out subject pronouns when they are unnecessary.

Here, the subject сестри is already stated, so adding вони would be redundant:

• Сестри довіряють... = perfectly natural
• Вони довіряють... = also possible in another context, but not needed here

Ukrainian relies heavily on the verb ending and the stated noun to show who is doing the action.

Because довіряють and сперечаються are two verbs with the same subject, joined by і (and).

This is a simple compound predicate:

• Сестри = subject
• довіряють and сперечаються = coordinated actions of that same subject

So no comma is needed:

• Сестри довіряють одна одній і рідко сперечаються.

A comma would usually appear only in more complex structures, not in a simple A and B pattern like this.