Learn Hardcore Norwegian: Jeg ser en sovende katt på sofaen.

In Norwegian, se can mean to see (notice/observe with your eyes) and takes a direct object: Jeg ser en katt = I see a cat.
Se på means to look at / watch (more deliberate or ongoing attention): Jeg ser på en katt = I’m looking at a cat / watching a cat.
So your sentence uses ser because it’s presenting what you see.

What does en mean here, and why is it en?

En is the indefinite article meaning a for common gender nouns.
Katt is common gender in Bokmål, so you say en katt (a cat).
(For neuter nouns you’d use et, e.g. et hus = a house.)

Could it also be ei katt?

Yes, in many varieties of Norwegian katt can be treated as feminine, so ei katt is possible—especially in speech and in dialects, and sometimes in writing depending on style.
In Bokmål, many feminine nouns can also be used as common gender, so en katt is very common and completely correct.

Why is the adjective sovende and not something like sover?

Sovende is a present participle used as an adjective, meaning sleeping (describing a noun): en sovende katt = a sleeping cat.
Sover is the present tense verb form: Katten sover = The cat is sleeping.
So you use sovende when it directly modifies katt.

How do adjective endings work here—why doesn’t sovende change?

Many Norwegian adjectives add endings for gender/number/definiteness (e.g. en stor katt, et stort hus, store katter).
But participles like sovende often behave like adjectives that don’t take the -t neuter ending and typically keep the same form in many common contexts.
You’ll very often see en/ei/et sovende … without changes.

Why is the adjective placed before the noun: en sovende katt?

In Norwegian, the default position for an adjective is before the noun:

en sovende katt = a sleeping cat
You can sometimes put descriptions after the noun in other constructions, but the normal, straightforward phrasing is adjective + noun.

Why is it på sofaen and not i sofaen?

På means on (on the surface): på sofaen = on the sofa.
I means in (inside/enclosed): i sofaen would sound like the cat is inside the sofa (e.g., stuffed down in it or inside its frame), which is usually not what you mean.

What does sofaen mean exactly, and why does it end in -en?

Sofaen means the sofa. The -en is the definite ending for a common gender noun in singular.

en sofa = a sofa
sofaen = the sofa
Norwegian often marks definiteness on the noun itself rather than using a separate word like the.

Why is it en katt (indefinite) but sofaen (definite)?

This is a very natural information pattern: you introduce a new animal as indefinite (a cat) but refer to the location as a specific, known thing (the sofa).
English does this too: I see a sleeping cat on the sofa.

What’s the word order rule in this sentence?

It follows the basic Norwegian main-clause order: Subject – Verb – Object – Adverbial:

Jeg (subject)
ser (verb)
en sovende katt (object)
på sofaen (place adverbial)

How would this change if I started with the location: On the sofa, I see…?

Norwegian main clauses follow the V2 rule: the finite verb must be in the second position. So if you front the place phrase, the verb stays second and the subject moves after it:

På sofaen ser jeg en sovende katt.
Not På sofaen jeg ser … (that would break V2).

How do I pronounce tricky parts like jeg, ser, and sovende?

It varies by dialect, but common (Eastern Norwegian / Oslo-like) approximations are:

jeg ≈ yai / yei (often not a hard g)
ser ≈ sair (a clear r, not English r)
sovende ≈ SOH-ven-deh (stress on the first syllable)
Also, Norwegian r is typically tapped or rolled, depending on region.

Can I drop en and just say Jeg ser sovende katt på sofaen?

Not in standard Norwegian. With a singular countable noun like katt, you normally need an article or some determiner: en/ei katt, katten, den katten, etc.
So keep en: Jeg ser en sovende katt på sofaen.