Jag vill skriva om både bokens huvudperson och vår lilla gräsmatta, men först måste jag hitta bokmärket och ta in spaden.

Here, skriva om is a fixed verb expression meaning to write about.

So:

• skriva = to write
• om = part of the expression skriva om = write about

Example:

• Jag skriver om Sverige. = I’m writing about Sweden.

A useful warning: skriva om can also mean rewrite, depending on context.

For example:

• Jag måste skriva om texten. can mean I have to rewrite the text

In your sentence, because it is followed by topics — både bokens huvudperson och vår lilla gräsmatta — the meaning is clearly write about.

både ... och ... means both ... and ....

In the sentence:

• både bokens huvudperson och vår lilla gräsmatta
• both the book’s main character and our little lawn

This structure is very common in Swedish.

Examples:

• Jag gillar både kaffe och te. = I like both coffee and tea.
• Hon talar både svenska och engelska. = She speaks both Swedish and English.

So både introduces the first item, and och introduces the second one.

Bokens huvudperson literally means the book’s main character.

This is a genitive construction:

• boken = the book
• bokens = the book’s
• huvudperson = main character

In Swedish, after a possessive or genitive word, the noun usually does not take the normal definite ending.

So Swedish says:

• bokens huvudperson
• min bil
• vår lärare

not:

• bokens huvudpersonen
• min bilen
• vår läraren

That is different from English, where we still say the book’s main character with the built into the phrase naturally.

Because vår (our) already makes the noun phrase definite in meaning.

In Swedish, possessives like:

• min = my
• din = your
• vår = our
• hans = his

usually replace the article.

So you say:

• vår lilla gräsmatta = our little lawn
• min gamla bil = my old car

not normally:

• den vår lilla gräsmattan

Also, after a possessive, the noun itself usually appears in the indefinite form:

• gräsmatta rather than gräsmattan

This is a very important Swedish pattern.

This is because adjectives often take the weak form after a definite determiner, including possessives like vår.

The adjective liten has irregular forms:

• liten = common gender singular indefinite
• litet = neuter singular indefinite
• små = plural
• lilla = weak/definite form

So:

• en liten gräsmatta = a small/little lawn
• vår lilla gräsmatta = our little lawn
• den lilla gräsmattan = the little lawn

So lilla appears because the phrase is definite in sense due to vår.

Because they refer to specific things: the bookmark and the shovel/spade.

In Swedish, the definite article is usually attached to the end of the noun:

• ett bokmärke = a bookmark

• bokmärket = the bookmark

• en spade = a shovel/spade
• spaden = the shovel/spade

So:

• hitta bokmärket = find the bookmark
• ta in spaden = bring in the shovel

This suggests the speaker has a particular bookmark and a particular shovel in mind, not just any bookmark or any shovel.

Ta in is a common verb phrase meaning bring in, take inside, or bring indoors, depending on context.

So:

• ta in spaden = bring the shovel inside

This is one of many Swedish verb + particle combinations, similar to English phrasal verbs.

Compare:

• ta av = take off
• ta på = put on
• ta med = take along
• ta in = bring/take in

In this sentence, ta in spaden probably means bringing the shovel indoors or putting it away from outside.

Both are possible, but they place the adverb först in slightly different positions.

Your sentence has:

• men först måste jag hitta bokmärket ...

This is very natural Swedish. When först is placed first, it gets extra emphasis:

• but first, I have to find the bookmark ...

Swedish is a V2 language, which means that in a main clause, the finite verb usually comes in the second position.

So after putting först first, the finite verb måste comes next:

• men
  • först
    • måste
      • jag ...

Compare:

• Jag måste först hitta bokmärket.
• Först måste jag hitta bokmärket.

Both are fine; the second one emphasizes first more clearly.

Because vill and måste are modal verbs, and modal verbs are followed by the bare infinitive in Swedish.

In the sentence:

• Jag vill skriva ...
• jag måste hitta ... och ta in ...

Here:

• vill
  • skriva
• måste
  • hitta
• måste also governs ta in

So the structure is:

• Jag vill skriva ...
• men först måste jag hitta ... och ta in ...

Just like in English:

• I want to write ...
• I must find ... and bring in ...

One difference is that Swedish usually does not use att after modal verbs:

• Jag måste gå. = I must go. not:
• Jag måste att gå.

Because both actions belong to the same subject and the same modal verb:

• måste jag hitta bokmärket och ta in spaden

This means:

• I have to find the bookmark and bring in the shovel

Swedish, like English, does not need to repeat the subject when the same subject performs both actions.

Compare:

• Jag måste läsa och skriva. = I have to read and write.
• Hon vill äta och sova. = She wants to eat and sleep.

You could repeat the subject in some situations, but it would usually sound unnecessary here.

Usually, yes. Gräsmatta is the normal Swedish word for lawn.

Literally, it is made up of:

• gräs = grass
• matta = mat/carpet

So it is like grass carpet, which matches the idea of a lawn very well.

In most everyday contexts, gräsmatta is the best translation of lawn.

Yes, it matters because gender affects articles and definite endings.

Here are the main nouns:

• bok = common gender (en bok)
• huvudperson = common gender (en huvudperson)
• gräsmatta = common gender (en gräsmatta)
• bokmärke = neuter (ett bokmärke)
• spade = common gender (en spade)

That is why you get:

• boken = the book
• bokens = the book’s
• gräsmatta after vår
• bokmärket = the bookmark
  because neuter nouns often take -et in the definite singular
• spaden = the shovel
  because common gender nouns often take -en in the definite singular

So gender helps explain the endings in the sentence.

It usually means main character or protagonist, depending on context.

Literally:

• huvud = head/main
• person = person

So huvudperson is the principal person in a story.

In many cases, English speakers would translate it as:

• main character

Sometimes:

• protagonist

But main character is often the safest everyday translation.