Jeg lægger bilnøglen i jakkelommen, så jeg ikke glemmer den, når vi åbner bagagerummet.

Here så means so or so that. It introduces the reason or purpose for the action:

Jeg lægger bilnøglen i jakkelommen, så jeg ikke glemmer den
= I put the car key in my jacket pocket so that I do not forget it.

So så is linking the two ideas: the action and its purpose.

Because så jeg ikke glemmer den is a subordinate clause.

In Danish, in subordinate clauses, sentence adverbs like ikke usually come before the finite verb:

• Main clause: Jeg glemmer den ikke
• Subordinate clause: ... så jeg ikke glemmer den

This is a very important Danish word-order pattern.

Because når introduces a subordinate clause, and subordinate clauses keep the normal order subject + verb:

• når vi åbner bagagerummet

If it were a main clause or direct question, the word order could be different:

• Hvornår åbner vi bagagerummet?

So after når, Danish does not use question word order.

Danish often uses the present tense for future meaning, especially after time words like når.

So:

• når vi åbner bagagerummet

can mean:

• when we open the trunk
• when we are going to open the trunk
• when we will open the trunk

This is normal Danish usage.

Because den refers back to bilnøglen, and bilnøgle is an en-word (common gender).

• en bilnøgle → bilnøglen
• pronoun: den

If the noun were an et-word, you would normally use det instead.

So den means it, but specifically for a noun with common gender.

Those endings are the Danish definite article attached to the noun.

Examples:

• en bilnøgle → bilnøglen = the car key
• en jakkelomme → jakkelommen = the jacket pocket
• et bagagerum → bagagerummet = the trunk

So instead of using a separate word like the, Danish often adds the definite ending directly to the noun.

Because Danish forms compound nouns by writing the parts together.

For example:

• bil + nøgle → bilnøgle
• jakke + lomme → jakkelomme
• bagage + rum → bagagerum

This is very common in Danish. English often writes similar ideas as two words or with more flexibility, but Danish strongly prefers one combined word.

Also, in Danish compounds, the last part usually decides the gender:

• nøgle is an en-word → en bilnøgle
• lomme is an en-word → en jakkelomme
• rum is an et-word → et bagagerum

Lægger is the present tense of lægge, which means to lay, to put, or to place something somewhere.

Here the speaker is actively placing the key in the pocket, so lægger is the right verb.

A very common contrast is:

• lægge = to put/place something
• ligge = to lie/be lying

So:

• Jeg lægger nøglen i lommen = I put the key in the pocket
• Nøglen ligger i lommen = The key is in the pocket

English speakers often mix these up, so this is a useful distinction to learn early.

Danish often leaves possession understood from context, especially when it is obvious whose item is meant.

So bilnøglen can naturally mean the car key in a context where it is clear that it is the speaker’s key, and jakkelommen can mean the jacket pocket where it is clear which jacket is meant.

If you want to be more explicit, you could say:

• min bilnøgle
• min jakkelomme

But the original sentence sounds natural without them.

Because glemmer and åbner are finite verbs in full clauses, not infinitives.

• så jeg ikke glemmer den = full clause
• når vi åbner bagagerummet = full clause

Danish uses at with the infinitive, for example:

• for ikke at glemme den = in order not to forget it

So in this sentence, at would not be correct before glemmer or åbner.

Not quite. In this sentence, når is the normal word for when because it refers to something that happens in the future or whenever something happens.

A useful contrast is:

• når = when, for repeated events or future situations
• da = when, for a specific event in the past

So here når is correct because the trunk-opening is not being described as one completed past event.