Ósmego czerwca moja siostra ma urodziny.

In this sentence, ósmego czerwca is a date used as a time expression, and Polish normally uses the genitive form for that.

So:

• ósmy = nominative form, like a basic dictionary-style form of eighth
• ósmego = genitive form, used here in the date expression

So Ósmego czerwca moja siostra ma urodziny means On the eighth of June, my sister has her birthday.

A useful contrast:

• Dziś jest ósmy czerwca. = Today is June eighth.
• Mam egzamin ósmego czerwca. = I have an exam on June eighth.

So the form depends on how the date is functioning in the sentence.

Because month names after a day number are normally put in the genitive in Polish.

• czerwiec = June in the basic form
• czerwca = of June / in June in date expressions

So:

• 8 czerwca = 8th of June / June 8
• read aloud in a sentence: ósmego czerwca

The same pattern works with other months too:

• 1 maja = 1st of May
• 15 sierpnia = 15th of August
• 20 grudnia = 20th of December

No. In Polish, a full date often appears without any preposition.

So English says:

• on June 8

But Polish can simply say:

• ósmego czerwca

That already means on the eighth of June.

Important contrast:

• w czerwcu = in June
• ósmego czerwca = on June 8

So w ósmego czerwca would be wrong here.

Because that is the normal Polish idiom.

Polish commonly uses the verb mieć (to have) with urodziny:

• mam urodziny = it’s my birthday / I have my birthday
• ma urodziny = it’s his/her birthday

So moja siostra ma urodziny is the natural way to say that your sister’s birthday falls on that day.

English usually says:

• My sister’s birthday is on June 8

Polish more naturally says:

• Moja siostra ma urodziny ósmego czerwca

Urodziny is normally a plural-only noun in Polish when it means birthday.

So Polish says:

• mam urodziny
• masz urodziny
• ona ma urodziny

even though English uses singular birthday.

A singular form urodzina is not what learners should use here.

If you really need a more singular-style expression, Polish can use:

• dzień urodzin = day of birth / birthday

But in everyday speech, urodziny is the standard word.

In this sentence, it means it is her birthday or her birthday falls on that date.

With a date expression like ósmego czerwca, the meaning is about the day itself, not necessarily the party.

So:

• Ósmego czerwca moja siostra ma urodziny. = My sister’s birthday is on June 8.

In other contexts, urodziny can sometimes refer to a birthday celebration too, but here the date makes the meaning clear.

Because moja siostra is the subject of the sentence, so it is in the nominative case.

• moja siostra = my sister as the subject
• mojej siostry = of my sister / my sister’s in the genitive

Here, the sentence is about what my sister has, so she is the subject:

• moja siostra ma urodziny

But if you wanted to say my sister’s birthday, you would use the genitive:

• urodziny mojej siostry

So:

• Moja siostra ma urodziny. = My sister has a birthday / It’s my sister’s birthday.
• Urodziny mojej siostry są w czerwcu. = My sister’s birthday is in June.

Yes. Polish word order is more flexible than English word order.

This sentence can also be said as:

• Moja siostra ma urodziny ósmego czerwca.

That is also natural.

The difference is mainly emphasis:

• Ósmego czerwca moja siostra ma urodziny.
  Emphasizes the date: On June 8...
• Moja siostra ma urodziny ósmego czerwca.
  Starts with the person and sounds a bit more neutral in many contexts.

So the original sentence is correct, but not the only possible order.

Because in Polish, month names are not capitalized.

So you write:

• czerwiec
• czerwca
• maj
• styczeń

not Czerwiec, Maj, etc., unless the word begins the whole sentence.

In your sentence, Ósmego is capitalized only because it is the first word of the sentence.
If the date appeared in the middle, it would usually be:

• moja siostra ma urodziny ósmego czerwca

The dictionary form is mieć, which means to have.

Here, ma is the 3rd person singular present tense form:

• mam = I have
• masz = you have
• ma = he/she/it has

So:

• moja siostra ma urodziny = my sister has a birthday / it is my sister’s birthday

A rough English approximation is CHERF-tsa.

A few useful details:

• cz sounds like ch in chop
• rz sounds like the s in measure or zh
• the w here is devoiced before c, so it sounds more like f
• ca sounds like tsa

So czerwca is pronounced approximately:

• CHERF-tsa

It may look intimidating, but it is a very common month form in dates.

Yes, you can think of it as a shortened date expression, historically connected to something like ósmego dnia czerwca — on the eighth day of June.

You do not need to say the longer version in normal speech, but this helps explain why the forms look the way they do:

• ósmego = genitive-type date form
• czerwca = genitive of czerwiec

So even though learners often memorize ósmego czerwca as a fixed chunk, there is a grammatical reason behind it.