Learn Hardcore Norwegian: Vi skal leie en leilighet med en stor stue neste år. - We shall rent an apartment with a big living room next year.

vil is more about desire or will (“we want to”).
kommer til å signals a prediction or something you believe will happen (“it’s going to happen”), but is less tied to a firm plan.
Example:
• Vi skal reise til Bergen (we have planned it).
• Vi vil reise til Bergen (we want to).
• Vi kommer til å reise til Bergen (I predict we will).

What does leie mean in Norwegian, and can it be both a verb and a noun?

leie as a verb means “to rent” or “to lease.” You can say å leie en leilighet (to rent an apartment).
As a noun, leie means “rent” (the payment): huset har høy leie (the house has high rent).
When you rent something out, you say å leie ut.

Why is the indefinite article en used before leilighet? Does this relate to gender?

In Bokmål there are two indefinite articles: en for common-gender nouns (masculine/feminine) and et for neuter nouns.

leilighet is a common-gender noun, so it takes en: en leilighet.
In Nynorsk or some dialects you might also see ei leilegheit, but in standard Bokmål it’s always en.

The sentence says en stor stue. Why is the adjective stor not inflected (for example, store or stort)?

Adjective endings in Norwegian depend on gender, number, and definiteness:

Common gender (en-words) indefinite singular: no ending (stor stue).
Neuter indefinite singular: t ending (stort rom).
Definite singular and all plurals: e ending (den store stuen, store rom).
Here both leilighet and stue are common-gender indefinite, so stor stays uninflected.

Why is the adjective placed before the noun in Norwegian? Is that always the case?

Yes—attributive adjectives (describing words) nearly always precede the noun they modify:
• en stor stue, et rødt hus, flotte stuer.
The only time the adjective follows is in predicative position (after a linking verb):
• Stuen er stor (The living room is large).

Why use med en stor stue instead of som har en stor stue (“which has a large living room”)?

Using med (“with”) is more concise and idiomatic for describing a feature.

en leilighet med en stor stue = “an apartment with a big living room.”
You can use a relative clause—en leilighet som har en stor stue—but it’s longer and often unnecessary.

Why is neste år placed at the end of the sentence? Can we move it elsewhere?

Norwegian follows a V2 word order (the verb is always the second element). Time expressions can go after the object (as here) or at the beginning:
• “Vi skal leie en leilighet … neste år.” (time at end)
• “Neste år skal vi leie en leilighet.” (time first, verb still second)

How would you say “We are going to rent the apartment” if you mean a specific one you’ve already mentioned?

Use the definite form by adding -en to the noun:
• Vi skal leie leiligheten.
If you also specify the living room:
• Vi skal leie leiligheten med den store stuen.

How do you form the plural of leilighet and stue, both in indefinite and definite forms?

Leilighet (fem. common gender):

Indefinite plural: leiligheter
Definite plural: leilighetene
Stue (fem. common gender):
Indefinite plural: stuer
Definite plural: stuene
Examples:
• Vi så mange leiligheter.
• Vi så de store leilighetene.