Siostry kłócą się tylko wtedy, gdy obie są zmęczone.

Because the sentence is about more than one sister.

• siostra = sister (singular)
• siostry = sisters (plural)

Here, siostry is the nominative plural, because it is the subject of the sentence.

Yes. Polish noun forms can overlap.

siostry can be:

• nominative plural = sisters
• genitive singular of siostra in some contexts = of the sister

But in this sentence, the verb is plural (kłócą się), so siostry clearly means sisters.

kłócą się comes from the verb kłócić się, which means to argue / to quarrel.

The się is part of the verb. Many Polish verbs are reflexive or reflexive-like, and you simply have to learn them that way.

So:

• kłócić się = to argue
• kłócą się = they argue

You should think of kłócić się as one vocabulary item, not as kłócić plus a separately translatable się.

Because the subject is they: the sisters.

The infinitive is kłócić się. In the present tense:

• ja kłócę się = I argue
• ty kłócisz się = you argue
• on/ona kłóci się = he/she argues
• my kłócimy się = we argue
• wy kłócicie się = you (plural) argue
• oni/one kłócą się = they argue

Since siostry is plural, Polish uses the 3rd person plural form: kłócą się.

It means only when.

Literally, it is built like this:

• tylko = only
• wtedy = then / at that time
• gdy = when

So the whole phrase tylko wtedy, gdy... is a very common Polish way to say only when...

You can think of it as:

• only then, when... which sounds unnatural in modern English, but helps show the structure.

Yes, kiedy is often possible, and both can mean when.

• gdy is a bit more neutral or slightly more formal/written
• kiedy is very common in speech too

So:

• Siostry kłócą się tylko wtedy, gdy obie są zmęczone.
• Siostry kłócą się tylko wtedy, kiedy obie są zmęczone.

Both are correct.

However, gdy fits very naturally in this type of sentence with a subordinate clause.

Because in Polish, subordinate clauses are normally separated by a comma.

Here, gdy obie są zmęczone is a subordinate clause: when both are tired.

So the comma is required:

• Siostry kłócą się tylko wtedy, gdy obie są zmęczone.

This is a normal and important punctuation rule in Polish.

obie means both, and it is the form used for feminine personal/non-masculine plural nouns.

Since siostry is feminine plural, obie agrees with it.

Compare:

• obaj = both (for masculine-personal groups, e.g. two men)
• obie = both (for two women, or non-masculine plural nouns)

So:

• obie siostry = both sisters
• obie są zmęczone = both are tired

You may also see obydwie, which means the same thing:

• obie
• obydwie

Both are correct.

Because the adjective has to agree with the subject.

The adjective is zmęczony = tired, but its ending changes depending on gender and number.

Here the subject is both sisters, so we need the feminine / non-masculine plural form:

• zmęczona = tired (singular feminine)
• zmęczony = tired (singular masculine)
• zmęczeni = tired (masculine-personal plural, e.g. men or mixed group)
• zmęczone = tired (feminine plural / non-masculine plural)

Since siostry are female, the correct form is zmęczone.

In standard Polish, są is normally required in the present tense.

• one są zmęczone = they are tired

Unlike Russian, Polish usually does not drop the present-tense form of to be in ordinary sentences.

So:

• obie są zmęczone = correct
• obie zmęczone = not a normal full sentence in standard Polish; it may sound incomplete or stylistically shortened

The sentence clearly refers to female people because of:

• siostry = sisters
• obie = both, feminine/non-masculine plural form
• zmęczone = tired, feminine/non-masculine plural form

Interestingly, the verb kłócą się itself does not show feminine gender in the present tense. The gender is shown by the noun and adjective forms, not by that verb form.

No, Polish word order is fairly flexible, but the original version is very natural.

The sentence:

• Siostry kłócą się tylko wtedy, gdy obie są zmęczone.

is a neutral, standard way to say it.

Other word orders may be possible, for example:

• Siostry tylko wtedy kłócą się, gdy obie są zmęczone.

But this can sound more marked or stylistically different. For learners, the original order is the safest one to use.

Yes, kłócić się is imperfective.

That matters because the sentence describes a general repeated situation:

• the sisters argue only when both are tired

In Polish, imperfective verbs are normally used for:

• repeated actions
• habits
• ongoing actions
• general truths or tendencies

A perfective verb would not fit well here, because the sentence is not about one completed argument, but about a recurring pattern.

A few parts may be difficult for English speakers:

• siostry — roughly SHOS-trih, though the Polish si is softer than English sh
• kłócą — roughly KWOO-tson with a nasal final vowel
• się — roughly shyeh with nasalization
• gdy — this is tricky; the gd cluster is pronounced together, roughly gdi or gdy, depending on accent and speed
• zmęczone — roughly zmen-CHO-neh, with nasalization in ę

The hardest features are often:

• nasal vowels like ą and ę
• consonant clusters like gdy
• soft consonants like si

Yes, sometimes Polish can drop the subject pronoun or even the subject noun if context makes it obvious.

For example, in conversation, someone might say:

• Kłócą się tylko wtedy, gdy obie są zmęczone. = They only argue when both are tired.

But if you want to state clearly that the subject is the sisters, keeping siostry is the most natural choice.

It sounds like a general rule or repeated pattern, not one single event.

That comes from:

• the present tense kłócą się
• the structure tylko wtedy, gdy...
• the imperfective verb kłócić się

So the sense is:

• this is when they tend to argue
• this is the condition under which arguments happen

It does not normally mean right now they are arguing because both are tired.