Barnet føler sig trygt, når forælderen er i rummet.

Barn means child in the indefinite form.

Barnet is the definite form, meaning the child. Danish usually adds the definite article to the end of the noun instead of putting a separate word in front:

• et barn = a child
• barnet = the child

The ending is -et because barn is a neuter noun: et barn.

Sig is a reflexive pronoun. In this sentence, føler sig trygt means feels safe.

In Danish, føle sig + adjective is a very common pattern for talking about how someone feels:

• Barnet føler sig trygt = The child feels safe
• Hun føler sig træt = She feels tired

The reflexive pronoun changes with person:

• jeg føler mig
• du føler dig
• han/hun/barnet føler sig

So sig here means something like himself / herself / itself, but in English we usually do not translate it directly in this kind of sentence.

Because barnet is a neuter noun, and the adjective agrees with it.

• et trygt barn = a safe/secure child
• barnet er trygt
• barnet føler sig trygt

If the subject were a common-gender noun, you would normally use tryg:

• Drengen føler sig tryg = The boy feels safe
• Pigen føler sig tryg = The girl feels safe

So the -t in trygt matches the neuter noun barnet.

Yes. Forælder means parent in the singular.

Forms:

• en forælder = a parent
• forælderen = the parent
• forældre = parents
• forældrene = the parents

So når forælderen er i rummet means when the parent is in the room.

If you wanted to say when the parents are in the room, it would be:

Når forældrene er i rummet.

Når is used for when in general, repeated, or expected situations.

Here it fits because the sentence describes a typical situation: The child feels safe when the parent is in the room.

Compare:

• når = when / whenever
  used for general truths, habits, and future situations

• da = when
  usually for one specific event in the past

• hvis = if
  for conditions

So:

• Barnet føler sig trygt, når forælderen er i rummet
  = a general or repeated situation

But:

• Barnet følte sig trygt, da forælderen var i rummet
  = one past situation

Because når introduces a subordinate clause, and subordinate clauses in Danish do not use normal main-clause inversion.

So after når, you get regular subject + verb order:

• når forælderen er i rummet

That is different from main clauses, where Danish normally follows the verb-second rule.

Main clause:

• Barnet føler sig trygt

Subordinate clause:

• når forælderen er i rummet

This is a very important Danish word-order pattern.

I rummet means in the room.

• rum = room
• rummet = the room

So:

• i rummet = in the room

The definite form suggests a specific room that is understood from the situation.

Compare:

• i rummet = in the room
• i et rum = in a room

You would not normally say i rum here.

Yes. A more explicitly general version would be:

Et barn føler sig trygt, når en forælder er i rummet.

That means A child feels safe when a parent is in the room.

The original sentence with barnet and forælderen can sound more like:

• a specific child and a specific parent already understood from context, or
• a general statement phrased in a more definite way

So both are possible, but the nuance is slightly different.

Then the main clause would show inversion, because Danish keeps the finite verb in second position in the main clause:

Når forælderen er i rummet, føler barnet sig trygt.

Notice the order:

• Når forælderen er i rummet = subordinate clause first
• føler barnet sig trygt = main clause with verb before subject

That is a very common Danish pattern.

It can be used with many adjectives. It is a very productive pattern in Danish.

For example:

• føle sig glad = feel happy
• føle sig træt = feel tired
• føle sig syg = feel ill
• føle sig tryg/trygt = feel safe / secure

So føler sig trygt is not an isolated phrase. It is part of a broader and very common structure.

Because Danish nouns belong to different genders.

• en forælder → forælderen
• et barn → barnet

So:

• common gender nouns usually take -en in the definite singular
• neuter nouns usually take -et in the definite singular

That is why the two nouns have different endings in the same sentence.