Learn Hardcore Norwegian: Morgenkåpen er myk, og verden virker stille mens vi går sakte til sengs. - The bathrobe is soft, and the world seems quiet as we walk slowly to bed.

Compound noun: morgen (“morning”) + kåpe (“coat/robe”) → morgenkåpe (“bathrobe”).
Definite form: In Bokmål common-gender nouns take -en as a suffix to mark “the …” → morgenkåpe → morgenkåpen (“the bathrobe”).

Why is the adjective myk used here, and not mykt?

Adjectives in Norwegian agree in gender (and sometimes number) with the noun they describe.

Kåpe is a common-gender noun (en-word), so its adjective takes the common form myk.
If the noun were neuter (et-word), e.g. teppe (“rug, blanket”), you would say teppet er mykt.
Plural and definite noun uses can change the ending further, but here it’s simply er myk.

What does virker mean in this context? I thought virke meant “to work” or “to function.”

Virke has two main senses:

“To function/work” (maskines virke – how a machine works)
“To seem/appear” (more literary)
In verden virker stille it means “seems” or “appears”, so you get:
“the world seems quiet.”

Why isn’t there an article before verden? Shouldn’t it be en verden or verdenen?

In Norwegian, you generally attach -en (common) or -et (neuter) to make a noun definite, but you don’t always use an explicit article word.
Verden here acts like a unique concept (“the world”), so it appears in its base (definite) form verden without a separate article.
You could also say hele verden (“the whole world”), but you never say verdenen.

What does mens mean? Is it related to the English word “men’s”?

No relation to English “men’s.” In Norwegian, mens is a conjunction meaning “while” or “as”, indicating simultaneous actions.
Example: Jeg sitter her mens du skriver = “I’m sitting here while you write.”

Why do we say gå til sengs instead of gå til sengen, and what’s the “s” on sengs?

Gå til sengs is a fixed, idiomatic expression meaning “go to bed.”
The -s on sengs is part of that frozen form; it’s not the regular genitive.
You won’t say til sengen here—use gå til sengs or the synonymous gå i seng or legge seg.

How do you pronounce the å in går and the ø in verden?

Approximate English equivalents:

å in går: [oː] – like the “o” in English “more” (but held longer).
ø in verden: [œ] or [øː] – somewhat like the “i” in British “bird” (without the final “r”) or the “u” in French “tu.”
The Norwegian r is typically a rolled or tapped sound.

Why is the adverb sakte placed after går? Could I say vi sakte går til sengs?

Norwegian main-clause word order is: Subject – Verb – Adverb – Object/Complement.

Vi går sakte til sengs follows that rule.
Vi sakte går … is grammatically understandable but unidiomatic.
You can front the adverb for emphasis or poetic style (Sakte går vi til sengs), but in neutral prose you put sakte after the verb.