Min søster vil gerne læse den nyeste roman i aften.

Because min already works as the determiner, like my in English.

In Danish, a possessive such as min usually replaces the article:

• søster = sister
• søsteren = the sister
• min søster = my sister

So you do not add en or the definite ending -en here.

That depends on the noun’s gender and number.

• min = common gender singular
• mit = neuter singular
• mine = plural

søster is a common gender singular noun, so min søster is correct.

Compare:

• min søster = my sister
• mit hus = my house
• mine søstre = my sisters

vil gerne is a very common Danish way to express wanting something.

Literally:

• vil = will / wants to
• gerne = gladly / willingly

But together, vil gerne often means:

• wants to
• would like to

So Min søster vil gerne læse... is a natural way to say that your sister wants or would like to read.

gerne makes the expression sound a little softer and more natural than just vil on its own.

Yes. That is grammatical.

But the tone changes a little:

• vil læse = wants to read / intends to read
• vil gerne læse = would like to read / wants to read, in a softer and more idiomatic way

In many everyday contexts, Danish prefers vil gerne where English might simply say wants to.

Because vil is a modal verb, and after modal verbs Danish normally uses the bare infinitive.

So:

• vil læse = wants to read
• not vil at læse

This is similar to English:

• wants to read uses to
• but can read, will read, must read do not

In Danish, after modal verbs like vil, kan, skal, må, you normally do not use at.

When a noun is definite and has an adjective before it, Danish normally uses this pattern:

den/det/de + adjective + noun

So:

• romanen = the novel
• den nyeste roman = the newest novel

You do not usually say den nyeste romanen.

This is a very important pattern in Danish:

• bilen = the car
• den store bil = the big car

Because roman is a common gender noun.

For definite noun phrases with an adjective:

• den = common gender singular
• det = neuter singular
• de = plural

So:

• den nyeste roman = the newest novel
• det nye hus = the new house

nyeste is the superlative form of ny.

• ny = new
• nyere = newer
• nyest = newest
• nyeste = the newest / newest in a definite phrase

Here it means the newest or the most recent.

So den nyeste roman means the newest novel or the latest novel, depending on context.

Usually no.

In Danish, roman normally means novel in the general sense, not specifically a romance novel.

So:

• en roman = a novel

If you want to be specific about a romance novel, you would normally use a more specific expression, such as en kærlighedsroman.

This is a common false friend for English speakers.

i aften is a fixed time expression meaning:

• tonight
• this evening

The noun aften means evening, and i is part of the expression.

Similar expressions include:

• i dag = today
• i morgen = tomorrow
• i aften = tonight / this evening

So even though English often uses one word (tonight), Danish uses the two-word phrase i aften.

Yes.

You can keep it at the end:

• Min søster vil gerne læse den nyeste roman i aften.

Or move it to the front:

• I aften vil min søster gerne læse den nyeste roman.

When you move something to the front in a Danish main clause, the finite verb still comes in second position. That is a basic Danish word-order rule often called V2 word order.

The tricky vowels here are:

• ø in søster
• æ in læse

There is no exact English equivalent for either sound.

A rough guide:

• ø is somewhat like the vowel in French peu or German schön
• æ is somewhat like the a in cat, but Danish pronunciation varies by accent and length

Also:

• the final -e in læse is usually a weak schwa sound
• søster is typically pronounced with a soft unstressed ending

The best approach is to listen to native audio and imitate it, because these vowels are hard to learn from English spelling descriptions alone.