Jag har en liten pump i garaget om du vill använda den hemma.

Because pump is a common-gender noun in Swedish, so it takes en.

• en pump = a pump
• pumpen = the pump

Adjectives must agree with the noun’s gender:

• en liten pump
• but ett litet hus

So since pump is an en-word, the correct form is en liten pump.

Liten is an irregular adjective. Its forms are:

• en liten noun
• ett litet noun
• små in the plural

So:

• en liten pump
• ett litet garage
• små pumpar

This is different from many regular adjectives, which often just add -t for ett nouns and -a in the plural.

Because Swedish usually needs the noun in a definite form here if you mean the garage.

• garage = garage
• garaget = the garage

So i garaget means in the garage.

In Swedish, definiteness is usually shown by adding an ending to the noun:

• en bil = a car
• bilen = the car
• ett garage = a garage
• garaget = the garage

Swedish nouns belong to one of two grammatical genders:

• common gender: en words
• neuter gender: ett words

There is no simple rule that always tells you which noun is which, so you usually have to learn the gender with the noun:

• en pump
• ett garage

That is why you get:

• i garaget
• but later använda den, because den refers to pump, which is an en-word

Because den refers back to pump.

In Swedish:

• den is used for en-words
• det is used for ett-words

Since pump is en pump, the correct pronoun is den:

• Jag har en liten pump ...
• ... om du vill använda den hemma.

If the noun were an ett-word, you would use det instead.

Here om means if, so om du vill means if you want.

• om = if
• du = you
• vill = want

So the phrase introduces a condition:

• Jag har en liten pump i garaget om du vill använda den hemma.
• I have a small pump in the garage if you want to use it at home.

Because Swedish modal verbs like vill are followed directly by the infinitive, without att.

• vill använda = want to use
• kan komma = can come
• ska läsa = will / going to read
• måste gå = must go

So:

• du vill använda den
• not du vill att använda den

This is similar to English want to use, except Swedish does not put a separate word here in this structure.

Because in this subordinate clause, the word order is the normal subject + verb pattern:

• om = if
• du = subject
• vill = verb
• använda den hemma = infinitive phrase

So:

• om du vill använda den hemma

This is different from main clauses in Swedish, where the finite verb usually comes second.

For example:

• Jag har en liten pump ...
  Here har is in second position.

But after om, you get a subordinate clause, so the structure is more straightforward.

Hemma means at home.

So:

• använda den hemma = use it at home

This is different from hem, which usually means home in the sense of direction:

• Jag går hem. = I’m going home.
• Jag är hemma. = I’m at home.

In your sentence, the meaning is location, not movement, so hemma is correct.

In this sentence, it most naturally refers to the listener’s home, because the speaker is offering the pump for the other person to use.

So the sense is:

• I have a small pump in the garage if you want to use it at home.

That usually implies at your place / in your home situation.

Still, hemma itself just means at home. Context tells you whose home is meant.

In modern Swedish, commas are generally used less than in English. A comma before a subordinate clause like om du vill använda den hemma is often optional and usually left out in ordinary writing.

So this is completely normal:

• Jag har en liten pump i garaget om du vill använda den hemma.

You might sometimes see a comma, especially if the writer wants a pause, but no comma is very standard.

Yes, but it would mean something slightly different in emphasis.

• Jag har en liten pump i garaget = I have a small pump in the garage.
• Jag har en liten pump hemma i garaget = I have a small pump at home, in the garage.

Adding hemma earlier can emphasize that the speaker has it at home, specifically in the garage.

In your original sentence, hemma belongs with använda den, so it describes where the other person might use the pump, not where the pump is kept.

Usually yes, but the exact kind of pump depends on context.

For example, it could mean:

• an air pump
• a bicycle pump
• a water pump
• some other kind of pump

The Swedish word pump is broad, just like the English word pump. The sentence itself does not specify which kind.