Når gæsterne er gået hjem, samler vi flasker og dåser på terrassen.

Yes. Når here means when in the sense of whenever / once / after the time that.

In this sentence, Når gæsterne er gået hjem means When the guests have gone home.

A useful contrast:

• når = when for something habitual, repeated, or seen as a general condition
• da = when about one specific event in the past

So if this is describing what people typically do after guests leave, når is the natural choice.

Gæsterne means the guests. The ending -ne is the definite plural ending.

So:

• en gæst = a guest
• gæsten = the guest
• gæster = guests
• gæsterne = the guests

Danish often puts definiteness at the end of the noun instead of using a separate word like the.

This is the present perfect:

• er = have/has (auxiliary)
• gået = gone
• hjem = home

So er gået hjem means have gone home.

Many motion verbs in Danish use være in older or more traditional-style grammar, but in modern standard Danish, gå normally forms the perfect with have: har gået when it means walked. However, in the expression gå hjem, Danish commonly uses er gået hjem meaning have gone home. For a learner, it is best to learn this whole expression as a set phrase.

Because gå hjem is an idiomatic expression meaning go home.

In Danish, hjem often appears without an article or preposition in this kind of phrase:

• gå hjem = go home
• komme hjem = come home
• tage hjem = go home / head home

So er gået hjem is not just have gone in a vague sense; it specifically means have gone home.

This is a very common Danish word-order pattern.

The sentence begins with a subordinate clause:

• Når gæsterne er gået hjem

After that comes the main clause. In Danish main clauses, the finite verb usually comes in second position. So when something other than the subject comes first, the verb comes before the subject:

• Når gæsterne er gået hjem, samler vi flasker og dåser på terrassen.

If the sentence started directly with the subject, it would be:

• Vi samler flasker og dåser på terrassen, når gæsterne er gået hjem.

Both are correct. The first version just puts the time clause first.

Because Danish often leaves plural nouns bare when speaking about unspecified things.

So:

• flasker og dåser = bottles and cans

This does not mean the bottles and the cans specifically; it just means bottles and cans in general, or the bottles/cans that are there to be collected.

English often does the same:

• We collect bottles and cans

So this part matches English quite closely.

Because på means on and is used for being on a surface or area like a terrace, balcony, island, etc.

• på terrassen = on the terrace / out on the patio

Using i would suggest being inside something, which does not fit a terrace.

So this is a normal preposition choice in Danish.

Yes, samler is present tense.

Danish often uses the present tense for:

• habitual actions
• general truths
• near-future or condition-based actions

So this sentence can mean something like:

• When the guests have gone home, we collect bottles and cans on the terrace
• or more naturally in English, Once the guests have gone home, we pick up the bottles and cans on the terrace

The Danish present tense is doing a job that English sometimes expresses with a future or more context-based translation.

Yes, often you can, but there is a nuance.

• gå hjem = go home
• tage hjem = go home / head home / leave for home

In many contexts, both work. But gå hjem is extremely common and often feels very natural in everyday speech.

So:

• Når gæsterne er gået hjem = when the guests have gone home
• Når gæsterne er taget hjem = when the guests have gone home / headed home

Both are possible, but the original sentence sounds perfectly normal.

Yes.

You can say:

• Når gæsterne er gået hjem, samler vi flasker og dåser på terrassen.
• Vi samler flasker og dåser på terrassen, når gæsterne er gået hjem.

The meaning is basically the same.

The difference is mostly emphasis:

• starting with Når gæsterne er gået hjem highlights the time condition first
• starting with Vi samler focuses first on what we do

A few parts may be difficult for English speakers:

• når: the å is like a broad o sound
• gæsterne: the æ is a front vowel, somewhat like the vowel in cat, but not exactly the same
• gået: the å is again the broad o-like vowel, and the word is often pronounced more smoothly than it looks
• dåser: again the å
• terrassen: stress is usually on the last main part: te-RAS-sen

The hardest part is often getting used to Danish vowels and reduced pronunciation, since many words sound less clearly pronounced than their spelling suggests.