Moja siostra gra na skrzypcach, a mój brat na flecie.

Because Polish adjectives and possessives must agree with the noun in gender, number, and case.

• siostra is feminine, so you use moja = my
• brat is masculine, so you use mój = my

So:

• moja siostra = my sister
• mój brat = my brother

This is very normal in Polish, unlike English, where my never changes.

Because in Polish, when you say that someone plays a musical instrument, you usually use:

grać na + instrument

So:

• grać na flecie = to play the flute
• grać na gitarze = to play the guitar
• grać na pianinie = to play the piano
• grać na skrzypcach = to play the violin

This is just the standard Polish pattern. English uses a direct object (play the violin), but Polish normally uses na with the instrument.

They are in the locative case because they follow na in this expression.

• na flecie → locative singular of flet
• na skrzypcach → locative plural of skrzypce

In this sentence, na goes with the locative because it is part of the fixed pattern grać na czymś when talking about instruments.

Because skrzypce is a plural-only noun in Polish. This is called pluralia tantum.

Even though in English violin is singular, in Polish the word is grammatically plural:

• dictionary form: skrzypce
• after na in this sentence: na skrzypcach

So Polish treats the violin as a plural noun in form, even when it refers to one instrument.

Other languages do this with some nouns too, just not usually with violin.

It is omitted because it is understood from the first part of the sentence.

Full version:

Moja siostra gra na skrzypcach, a mój brat gra na flecie.

Shorter, more natural version:

Moja siostra gra na skrzypcach, a mój brat na flecie.

This kind of omission is very common in Polish when the verb is obvious from context. English can do something similar:

• My sister plays the violin, and my brother the flute.

Even if that sounds a bit more literary in English, it is perfectly natural in Polish.

Not exactly.

In this sentence, a means something like:

• and
• while
• whereas

It often connects two ideas with a slight contrast or comparison.

So:

Moja siostra gra na skrzypcach, a mój brat na flecie. = My sister plays the violin, and my brother plays the flute with a mild sense of by contrast / while.

Compare:

• i = simple and
• a = and / while / whereas, often contrasting two facts

Here a is the more natural choice because the sentence compares what the sister plays and what the brother plays.

Because in Polish, a is normally preceded by a comma when it joins two clauses or two contrasted parts of a sentence.

So the punctuation here is standard:

Moja siostra gra na skrzypcach, a mój brat na flecie.

This is one of the places where Polish punctuation is stricter than English.

Yes, this word order is natural and neutral.

The sentence:

Moja siostra gra na skrzypcach, a mój brat na flecie.

sounds like a normal, everyday statement.

Polish word order is flexible, so other orders are possible, but they may change the emphasis. For example:

• Na skrzypcach gra moja siostra, a na flecie mój brat.
  This emphasizes the instruments more.

• Mój brat gra na flecie, a moja siostra na skrzypcach.
  Same basic meaning, different order of information.

The original sentence is probably the best neutral version for a learner.

Usually, no. For musical instruments, Polish normally uses grać na.

So the correct standard form is:

• grać na skrzypcach
• grać na flecie

Saying gra skrzypce would sound wrong in standard Polish.

Not really. Although na often literally means on, in this sentence you should treat grać na as a set expression meaning to play an instrument.

So it is better not to translate word by word.

• grać na flecie = to play the flute
• not literally to play on the flute in normal English

This is a good example of where Polish and English structure the idea differently.

Here are the dictionary forms:

• moja → base possessive form is mój
• siostra → sister
• gra → from grać = to play
• na → preposition
• skrzypcach → base form skrzypce = violin
• a → and / whereas
• mój → my
• brat → brother
• flecie → base form flet = flute

This is useful because some words appear in changed forms, especially skrzypcach and flecie, due to case.