Hon vill laga kyckling med morötter i kväll.

Because vill is a modal verb here. In Swedish, modal verbs are normally followed by the bare infinitive:

• hon vill laga = she wants to cook
• hon kan laga = she can cook
• hon måste laga = she must cook

So Swedish says vill laga, not vill att laga.

Vill is the present tense of vilja, meaning to want.

So:

• hon vill = she wants

In this sentence, vill laga means wants to cook.

Here, laga means to cook or to prepare food.

A very common expression is:

• laga mat = cook food

But laga can also mean repair/fix in other contexts:

• laga bilen = repair the car
• laga maten = cook the food

So the meaning depends on context. Since the sentence is about kyckling and morötter, it clearly means cook.

In food contexts, Swedish often uses the noun without an article when talking about a dish or ingredient in a general way.

So:

• laga kyckling = cook chicken
• äta fisk = eat fish
• köpa bröd = buy bread

If you said en kyckling, it would more strongly suggest a whole chicken or the animal as one countable item.

So laga kyckling sounds natural for cook chicken as food.

Because morötter here means carrots in a general, non-specific sense.

Swedish often leaves out the article with indefinite plural nouns when speaking generally:

• med morötter = with carrots
• med potatis = with potatoes
• med tomater = with tomatoes

If you wanted to refer to specific carrots already known in the conversation, you might say:

• med morötterna = with the carrots

It most naturally means that the chicken is being cooked or served with carrots.

So the phrase can be understood as:

• cook chicken with carrots
• chicken as the main dish, carrots as part of the dish/meal

In practice, English and Swedish work similarly here. It does not usually cause confusion.

Because the basic noun is en morot = a carrot, and the plural is:

• morot → morötter

So:

• en morot = a carrot
• morötter = carrots

The vowel changes in the plural, which is something learners just have to get used to with many Swedish nouns.

I kväll means this evening or tonight.

Swedish often uses i in time expressions like this:

• i dag = today
• i morgon = tomorrow
• i kväll = this evening / tonight

So the i is just part of the normal expression.

Yes. I kväll and ikväll are both used.

In modern Swedish, the one-word form ikväll is very common, but the two-word form i kväll is also accepted.

So these are both fine:

• Hon vill laga kyckling med morötter i kväll.
• Hon vill laga kyckling med morötter ikväll.

Yes, i kväll can come first.

The sentence you have is the normal subject + verb order:

• Hon vill laga kyckling med morötter i kväll.

But Swedish also allows the time expression at the beginning:

• I kväll vill hon laga kyckling med morötter.

When something other than the subject comes first in a Swedish main clause, the finite verb still stays in second position. That is a very important Swedish word-order rule.

So:

• Hon vill ...
• I kväll vill hon ...

Both are correct.

In this sentence, it most naturally means chicken meat.

Swedish uses kyckling both for:

• a chicken/chick as an animal
• chicken as food

The context makes the meaning clear. Since the sentence uses laga and mentions morötter, it clearly means food.

A rough guide is SHYCK-ling, but that is only approximate.

A few things are tricky for English speakers:

• ky often has a soft sound, somewhat like sh mixed with a rounded vowel
• ckl in the middle can feel compact and fast
• the stress is on the first syllable: KYCK-ling

You do not need a perfect English-style spelling to learn it, but it is good to know that ky is not pronounced like English kai.

The finite verb vill is in the present tense.

So literally, the sentence is in the present, but in meaning it refers to a current wish about the future:

• Hon vill laga ... i kväll = She wants to cook ... tonight

This is normal in both Swedish and English.