Když má moje sestra hlad, nejraději jí brambory s cibulí a rajčetem.

Czech often expresses physical states with mít + a noun.

So:

• mít hlad = literally to have hunger = to be hungry
• mít žízeň = to be thirsty
• mít strach = to be afraid

So Když má moje sestra hlad is the normal Czech way to say When my sister is hungry.

Když means when here.

It introduces a subordinate clause:

• Když má moje sestra hlad, ... = When my sister is hungry, ...

Depending on context, když can also mean if in some everyday sentences, but in this example when is the natural meaning.

Because Když má moje sestra hlad is a subordinate clause, and Czech normally separates subordinate clauses with a comma.

So the structure is:

• Když má moje sestra hlad, = subordinate clause
• nejraději jí brambory s cibulí a rajčetem. = main clause

This is similar to English, where a comma is also common after an introductory when clause.

Nejraději means something like most gladly, preferably, or likes best.

It comes from:

• rád / ráda = glad, likes
• raději = rather, preferably
• nejraději = most preferably, likes best

In this sentence, nejraději jí means she most likes to eat or more naturally she likes eating ... best.

It is very common in Czech to use nejraději to talk about preferences:

• Nejraději piju čaj. = I like tea best.
• Nejraději chodíme pěšky. = We prefer to go on foot.

Here jí is the verb eats.

It is the 3rd person singular form of jíst:

• já jím = I eat
• ty jíš = you eat
• on/ona/ono jí = he/she/it eats

So:

• nejraději jí brambory = she likes eating potatoes best

This can confuse learners because jí can also be a pronoun form meaning to her or sometimes her in certain contexts. You tell the difference from the sentence structure.

Here it is clearly a verb because it is followed by a direct object:

• jí brambory = eats potatoes

Because Czech normally uses the plural when talking about potatoes as food in the general sense.

• brambora = one potato
• brambory = potatoes

So jí brambory is the natural way to say she eats potatoes.

If you used the singular, it would usually mean one individual potato:

• jí bramboru = she is eating a potato

Because the preposition s meaning with requires the instrumental case.

So:

• cibule → s cibulí
• rajče → s rajčetem

That is why the nouns do not stay in their dictionary forms.

This is a very common pattern:

• s kamarádem = with a friend
• s vodou = with water
• s maminkou = with mom

Because they belong to different noun types and genders, so their instrumental singular endings are different.

• cibule is a feminine noun, so instrumental singular is cibulí
• rajče is a neuter noun, so instrumental singular is rajčetem

The case is the same, but the endings depend on the noun’s declension pattern.

So the important idea is:

• same case
• different noun classes
• therefore different endings

Yes. Both are possible.

• moje sestra = my sister
• má sestra = my sister

Má is often a bit shorter and very common in everyday speech.
Moje can sound a little fuller or slightly more emphatic in some contexts, but in many sentences the difference is small.

So this sentence could also be:

• Když má má sestra hlad, nejraději jí brambory s cibulí a rajčetem.

That is grammatically correct, although má má sestra puts two similar-looking words next to each other, which some learners find awkward to read at first.

They are completely different words, even though they look similar.

• má = has
  This is the verb mít in 3rd person singular.
• moje = my
  This is a possessive pronoun.

So in:

• Když má moje sestra hlad

the parts are:

• má = has
• moje sestra = my sister
• hlad = hunger

Literally: When my sister has hunger

Yes, Czech word order is fairly flexible, but the version in the sentence is natural.

• nejraději jí brambory = she likes eating potatoes best

You could also hear:

• Moje sestra nejraději jí brambory...
• Brambory s cibulí a rajčetem jí moje sestra nejraději.

These variations change the emphasis more than the basic meaning.

In the original sentence, the word order is neutral and easy to understand: first the condition, then the preference, then the food.

No, you do not have to repeat it.

• s cibulí a rajčetem = perfectly normal
• s cibulí a s rajčetem = also possible

When one preposition applies to two coordinated nouns, Czech often uses it just once.

So the original sentence is fully natural.

Here jí is pronounced with a long í sound, roughly yee with a long vowel.

A rough pronunciation of the whole phrase:

• nejraději jí ≈ nay-rad-yeh-yi yee

A few notes:

• j in Czech sounds like English y
• í is long
• ě in raději affects the pronunciation of the preceding consonant and gives a ye-like sound

So jí the verb is not pronounced like English gee or jai; it is closer to yee.

Yes, grammatically it is fine and understandable.

The only small point is style: in very natural everyday English, the translation often sounds smoother as When my sister is hungry, she likes potatoes with onion and tomato best or she prefers potatoes with onion and tomato. Czech often uses nejraději in places where English might use prefers or likes best.

So as Czech, the sentence is normal; just remember that the most natural English equivalent may not match it word for word.