Jag köper ett kilo jordgubbar, men min syster vill bara ha lite sylt.

Because kilo is a neuter noun in Swedish, so it takes ett.

• ett kilo = a kilo
• två kilo = two kilos

This is because kilo is short for kilogram, and kilogram is also an ett word.

Because the sentence is talking about an indefinite amount of strawberries: one kilo of strawberries, not the strawberries.

After quantities, Swedish usually uses the indefinite plural:

• ett kilo jordgubbar = a kilo of strawberries
• två liter äpplen would be wrong, because apples are countable in another way, but the pattern with quantity + indefinite noun is the same idea
• ett paket kakor = a packet of cookies

So jordgubbar here is just the normal plural form, not the definite plural.

Because Swedish usually does not need a word like of in this kind of expression.

English says:

• a kilo of strawberries

Swedish says:

• ett kilo jordgubbar

This is very common with measurements and containers:

• ett glas vatten = a glass of water
• en kopp kaffe = a cup of coffee
• ett kilo potatis = a kilo of potatoes

So this structure is completely normal in Swedish.

When a noun has a possessive like min, din, hans, hennes, vår, or deras, Swedish normally uses the indefinite form of the noun.

So:

• min syster = my sister
• din bok = your book
• hennes bil = her car

Not:

• min systern
• din boken

The possessive already makes the noun specific, so Swedish does not also add the definite ending.

Yes, ha does mean have, but vill ha is a very common expression meaning want or want to have.

So:

• Jag vill ha kaffe. = I want coffee.
• Hon vill ha en ny cykel. = She wants a new bike.

In your sentence:

• min syster vill bara ha lite sylt = my sister only wants a little jam

It sounds very natural in Swedish. In many contexts, vill ha is the normal way to express wanting something.

Because in Swedish main clauses, sentence adverbs like bara often come after the finite verb and before the infinitive.

Here:

• vill is the finite verb
• ha is the infinitive
• bara goes between them

So:

• hon vill bara ha lite sylt

This placement means she only wants a little jam.

Compare:

• Jag kan inte komma. = I cannot come.
• Hon vill gärna äta. = She would like to eat.
• Vi ska bara titta. = We are only going to look.

This is a very common Swedish word-order pattern.

Because sylt is being treated as an uncountable substance here, like jam in English.

You usually do not count jam as separate items, so Swedish uses:

• lite sylt = a little / some jam

Not usually:

• en sylt

That would sound odd in most contexts, just like a jam sounds odd in English unless you mean a specific type or jar in a special context.

Here, lite means a little or some.

So:

• lite sylt = a little jam / some jam

It is often used with uncountable nouns:

• lite vatten = a little water
• lite socker = a little sugar
• lite kaffe = a little coffee / some coffee

It can also sometimes mean not very much in a more general sense.

In this sentence, bara ha lite sylt suggests that the sister wants only a small amount.

Yes. Swedish present tense often covers both simple present and present continuous, depending on context.

So Jag köper can mean:

• I buy
• I am buying

In this sentence, the natural English translation is probably I’m buying a kilo of strawberries, but Swedish does not need a separate form like English am buying.

Because men means but, and Swedish often uses a comma before it when joining two main clauses.

Here you have:

• Jag köper ett kilo jordgubbar
• men min syster vill bara ha lite sylt

Both parts could stand as full sentences, so the comma is natural and standard.

Usually, yes. In this sentence it clearly means but and contrasts the two ideas:

• I’m buying a kilo of strawberries,
• but my sister only wants a little jam.

It is one of the most common Swedish conjunctions.

Because they are being treated differently grammatically.

• jordgubbar is a countable noun in plural: strawberries
• sylt is an uncountable mass noun here: jam

So Swedish says:

• ett kilo jordgubbar = a kilo of strawberries
• lite sylt = some jam

This is very similar to English:

• strawberries is plural
• jam is usually uncountable

It might be understood, but vill bara ha is the more natural word order.

The standard, natural version is:

• min syster vill bara ha lite sylt

That is the usual placement of bara with a finite verb plus infinitive. Swedish word order is often quite fixed in these patterns, so it is best to learn vill bara ha as a chunk.

The sentence is already perfectly correct, but if you wanted a slightly more formal tone, you might replace bara with endast:

• Jag köper ett kilo jordgubbar, men min syster vill endast ha lite sylt.

That said, bara is much more common in everyday speech, and it sounds completely natural here.

Usually sylt is best translated as jam or sometimes preserve.

In everyday Swedish, sylt is the normal word for sweet fruit preserves such as:

• jordgubbssylt = strawberry jam
• hallonsylt = raspberry jam

So in this sentence, lite sylt simply means a little jam.