Jag vill översätta den här texten till engelska.

Because vill is a modal verb, and modal verbs in Swedish are followed by the infinitive without att.

So:

• Jag vill översätta = I want to translate
• not Jag vill att översätta

This is different from English, where you need to after want.

A few similar examples:

• Jag kan läsa. = I can read.
• Jag ska skriva. = I will/am going to write.
• Jag vill förstå. = I want to understand.

So översätta is the infinitive here.

In a normal Swedish main clause, the finite verb usually comes in the second position. Here the sentence starts with the subject Jag, so the finite verb vill comes next.

Pattern:

• Jag = subject
• vill = finite verb
• översätta den här texten till engelska = the rest of the sentence

This is the standard basic order for a simple statement.

Because text is an en-word in Swedish:

• en text
• therefore den här texten

Swedish demonstratives must match the gender/number of the noun:

• den här for common gender singular en-words
• det här for neuter singular ett-words
• de här for plural

Examples:

• den här boken = this book
• det här huset = this house
• de här böckerna = these books

Since text is common gender, den här is correct.

Because Swedish commonly uses double definiteness with this kind of demonstrative expression.

So in everyday Swedish you say:

• den här texten
• literally something like this the-text

That may feel strange to an English speaker, but it is normal Swedish grammar.

Compare:

• text = a text
• texten = the text
• den här texten = this text

So the noun usually stays in the definite form after den här / det här / de här.

By itself, här means here. But in the pattern den här / det här / de här, it helps form the meaning this / these.

So:

• den här texten = this text
• det här ordet = this word
• de här meningarna = these sentences

You can think of den här as a very common spoken and everyday way to say this.

Yes. Denna text is also correct.

The difference is mostly style:

• den här texten = more common in everyday speech
• denna text = often a bit more formal or more written

Both can mean this text.

So these are both possible:

• Jag vill översätta den här texten till engelska.
• Jag vill översätta denna text till engelska.

Because till is used here to show the target language: the language you are translating into.

So:

• översätta ... till engelska = translate ... into English
• översätta ... till svenska = translate ... into Swedish

This is the natural choice after översätta when you mean the result should be in that language.

Usually, not in this sentence.

With översätta, Swedish normally uses till for the target language:

• översätta texten till engelska = translate the text into English

But på engelska is used when something is in English:

• Texten är på engelska. = The text is in English.
• Kan du säga det på engelska? = Can you say it in English?

So a useful distinction is:

• till engelska = into English
• på engelska = in English

Because language names are usually used without the definite ending in this kind of expression.

So you say:

• till engelska
• på svenska
• från tyska

The definite form engelskan can exist, but it is used in other contexts, for example when talking about the English language as a subject or system:

• Engelskan är svår ibland. = English is difficult sometimes.

But after till in a phrase like this, the normal form is simply engelska.

Because in Swedish, names of languages are usually written with a lowercase letter, unless they begin the sentence.

So Swedish writes:

• engelska
• svenska
• tyska

This is different from English, where you write English, Swedish, German with capitals.

The ending -en is the definite singular ending for this noun.

So:

• en text = a text
• texten = the text

Many common-gender nouns take -en in the definite singular, though not all nouns behave exactly the same way.

In this sentence, texten is definite because it is part of den här texten.

Yes, it is very natural.

A native speaker would commonly say:

• Jag vill översätta den här texten till engelska.

You could also hear slightly different choices depending on tone or context, but this sentence is fully normal and idiomatic Swedish.