Learn Hardcore Norwegian: Etter å ha logget inn på nettbanken ser han at husleien allerede er betalt. - After having logged in to the online bank he sees that the rent is already paid.

Using “etter å logge inn” would sound wrong or at best very unusual; the infinitive å logge on its own does not express that the action is completed before the next action. The “å ha + past participle” structure is the perfect infinitive, and it makes it clear that the logging-in happened before he sees that the rent is paid.

A full finite-clause alternative would be:

Etter at han hadde logget inn på nettbanken, …
(After he had logged in to the online bank, …)

What is the function of “etter å ha logget inn på nettbanken” in the sentence?

The whole phrase “etter å ha logget inn på nettbanken” is an adverbial phrase of time. It answers the question “When does he see it?”:

Når ser han det?
– Etter å ha logget inn på nettbanken.

Because it is placed first, it occupies the first position in the main clause, and that triggers the typical Norwegian verb‑second word order in the rest of the sentence:

First element: Etter å ha logget inn på nettbanken
Second element (finite verb): ser
Third element (subject): han
The rest: at husleien allerede er betalt.

Why is it “ser han” and not “han ser” after the comma?

Norwegian main clauses usually follow a V2 rule (verb-second word order):

The finite verb must be in second position, no matter what comes first.

If the adverbial phrase doesn’t come first, you get normal-looking English-like order:

Han ser at husleien allerede er betalt.
(He sees that the rent has already been paid.)

But when you put an adverbial first:

Etter å ha logget inn på nettbanken ser han at husleien allerede er betalt.
(1st: Etter å ha logget inn på nettbanken, 2nd: ser, 3rd: han)

“Etter å ha logget inn på nettbanken han ser …” would break the V2 rule and sound ungrammatical.

Could I start with “Han ser …” instead? Would the meaning change?

Yes, you can reorder the sentence:

Han ser at husleien allerede er betalt etter å ha logget inn på nettbanken.

This is grammatically fine and means the same thing. Differences:

Original:
Etter å ha logget inn på nettbanken ser han at husleien allerede er betalt.
– Emphasizes the time / sequence: first log in, then see.
Alternative:
Han ser at husleien allerede er betalt etter å ha logget inn på nettbanken.
– Focus is more on what he sees, with the “after logging in” added at the end.

Both are natural; the original feels slightly more narrative: After logging in, he then notices…

What does “nettbanken” literally mean, and why does it end in -en?

Nettbanken is:

nett (net / online) + bank (bank) + the definite article -en
→ nettbanken = the online bank / the internet bank

In Norwegian, the definite article is usually a suffix, not a separate word:

en bank = a bank
banken = the bank
nettbank = online bank
nettbanken = the online bank

So på nettbanken means on / in the online bank (website/app).

Why is it “på nettbanken” and not “i nettbanken”?

Both “på nettbanken” and “i nettbanken” can be heard in real life, and both will be understood.

Common tendencies:

i nettbanken:
Often understood as inside the internet banking system, the environment you see after logging in.
på nettbanken:
Influenced by expressions like på nettet (on the internet). It can sound more colloquial in some dialects.

Many banks themselves use:

logge inn i nettbanken

But the sentence you have with på nettbanken is still natural and acceptable. Prepositions with digital services are somewhat fluid in modern Norwegian.

What exactly is “husleien”? How is it formed?

Husleien is:

hus (house) + leie (rent) → husleie (house rent = rent, as in what you pay for housing)
plus the definite ending -n / -en → husleien = the rent

Compare forms:

husleie – rent (indefinite)
husleien – the rent (definite)

So husleien er betalt = the rent is paid.

You might also see husleia as an alternative definite form in Bokmål (more informal / spoken style), especially in Norway:

husleia er betalt – same meaning.

Why is it “allerede er betalt” and not “allerede har blitt betalt” or “allerede har betalt”?

There are a few structures here that matter:

er betalt
- This is a stative / resultative passive:
  husleien er betalt = the rent is (now) paid → focuses on the resulting state.
har blitt betalt
- This is a dynamic passive in the perfect tense:
  husleien har blitt betalt = the rent has been paid → focuses on the completed action of paying.
har betalt
- This is active voice, requires a subject that did the paying:
  Han har betalt husleien. = He has paid the rent.

In your sentence:

ser han at husleien allerede er betalt.

The focus is on the state he observes: at the moment he looks, the rent is already in a paid state. That makes “er betalt” very natural.

You could say:

… ser han at husleien allerede har blitt betalt.

This is also correct but puts a bit more emphasis on the completed event (“has been paid”) rather than just the state.

Where can “allerede” go in this part: “husleien allerede er betalt”? Are other word orders possible?

Yes, adverbs like allerede (already) are quite flexible. Some common options here:

… at husleien allerede er betalt.
… at husleien er allerede betalt. (possible but less neutral in many dialects)
… at husleien er betalt allerede.

The most standard and natural in written Bokmål is usually:

husleien allerede er betalt

husleien er allerede betalt

Putting allerede early in the clause (right after the subject or just after “at”) is very typical:

Han ser at husleien allerede er betalt.
Han ser allerede at husleien er betalt. (now he is already seeing it)

What is the difference between “etter å ha logget inn …” and “etter at han har logget inn …”?

Both express a time relationship (after he has logged in), but structurally they’re different:

etter å ha logget inn på nettbanken
- Infinitive construction (no explicit subject; understood from context)
- Compact and stylistically smooth.
etter at han har logget inn på nettbanken
- Subordinate clause with its own subject (han) and verb (har logget)

Both are grammatically correct:

Etter å ha logget inn på nettbanken ser han at …
Etter at han har logget inn på nettbanken ser han at …

The first sounds a bit more formal / written and more compressed. The second is more explicit and can sound a bit more conversational or explanatory.

How would the sentence change if everything happened in the past (not present)?

Right now the main verb is present tense:

ser han = he sees

To move the whole situation into the past, you’d usually change ser to så (past tense of å se):

Etter å ha logget inn på nettbanken så han at husleien allerede var betalt.

Changes:

ser → så (se in the past)
er betalt → often var betalt (was paid), matching the past time frame

So a good past-tense version is:

Etter å ha logget inn på nettbanken så han at husleien allerede var betalt.
(After logging into the online bank, he saw that the rent was already paid.)

Why do we need “inn” in “logget inn”? Could we just say “logget”?

In Norwegian, “å logge (seg) inn” is a phrasal verb (verb + particle):

å logge inn = to log in (sign into a system)
å logge på = also “to log on” (often similar meaning in computer context)

If you only say “å logge”, it usually means to keep a log / record (like logging work hours, logging data), not specifically signing into a system.

So:

Han logget inn på nettbanken.
→ He signed into / logged into his online bank.
Han logget timene sine.
→ He logged his hours.

In your sentence, inn is necessary to get the “log in” meaning.

Is the sentence formal, informal, or neutral? Are there more colloquial variants?

The sentence:

Etter å ha logget inn på nettbanken ser han at husleien allerede er betalt.

is neutral standard Bokmål. It’s fine in both written and spoken language, maybe slightly on the written/neutral side because of the etter å ha + participle structure.

A bit more colloquial/spoken variants might be:

Når han logger inn i nettbanken, ser han at husleia allerede er betalt.
(using når instead of etter å ha, and husleia instead of husleien)
Etter at han har logga inn i nettbanken, ser han at husleia allerede er betalt.
(spoken-style endings like logga and husleia)

But your original version is perfectly natural, clear, and correct.