Jeg går udenfor for at trække vejret i den friske luft.

Går is the present tense of at gå.

In this sentence, it most naturally means go:
Jeg går udenfor = I’m going outside / I go outside.

Danish at gå can mean both:

• to walk
• to go

Which meaning it has depends on context. Here, the important idea is that the speaker is moving outside, not necessarily that they are walking on foot for a long distance.

So this sentence is very natural Danish, even though English would often prefer I’m going outside rather than I’m walking outside.

Yes. Jeg går is present tense.

Like the English present, Danish present tense can cover more than one idea depending on context:

• I go outside
• I am going outside
• sometimes even a near-future idea like I’m about to go outside

So Jeg går udenfor for at trække vejret i den friske luft can very naturally mean I’m going outside to breathe in the fresh air.

Here udenfor means outside.

As one word, udenfor is an adverb:

• Jeg går udenfor = I’m going outside

This is different from uden for as two words, which usually means outside of or not within something:

• uden for huset = outside the house
• uden for byen = outside the city

So in your sentence, udenfor is one word because it stands alone as outside, not outside of something.

For at means to or in order to before an infinitive.

So:

• for at trække vejret = to breathe
• more literally: in order to breathe

This structure is very common in Danish when you explain purpose:

• Jeg går udenfor for at få luft = I go outside to get some air
• Jeg læser for at lære = I read to learn

English often uses just to, but Danish often uses for at in this kind of purpose clause.

Yes, it is an idiom.

At trække vejret means to breathe.

Literally, trække means pull or draw, so the expression is something like draw breath. English has something similar in more literary language, but in modern Danish this is the normal everyday way to say breathe.

So:

• Jeg trækker vejret = I breathe / I am breathing
• Han kan ikke trække vejret = He can’t breathe

It is best to learn trække vejret as a fixed expression.

In the fixed expression trække vejret, Danish uses the definite form vejret.

So the standard idiom is:

• at trække vejret = to breathe

not normally:

• at trække vejr

This is just how the expression is built. Many learners notice that vejret looks like the weather, and that is not a coincidence historically, but in modern Danish you should mainly think of trække vejret as one whole unit meaning breathe.

Formally, yes: vejret is also the definite form of vejr, which usually means weather.

For example:

• Vejret er godt = The weather is good

But in trække vejret, the phrase does not mean anything like pull the weather. It is simply a fixed idiomatic expression meaning breathe.

So learners should avoid translating it word by word. Just memorize:

• at trække vejret = to breathe

I den friske luft means in the fresh air.

This is a definite noun phrase:

• luft = air
• frisk luft = fresh air
• den friske luft = the fresh air

In Danish, when a common-gender noun is definite and has an adjective, you usually get:

• den + adjective + noun with definite ending

So:

• den friske luft

because luft is a common gender noun.

You may also hear få frisk luft without den, especially in phrases like:

• Jeg går udenfor for at få frisk luft = I’m going outside to get fresh air

That version is also very natural. In your sentence, i den friske luft sounds a bit fuller and more descriptive: in the fresh air.

Because luft is a common gender noun in Danish, not a neuter noun.

Danish has two genders:

• common gender → uses en / den
• neuter → uses et / det

Since it is:

• en luft
  the definite phrase becomes:
• den friske luft

If it were a neuter noun, you would use det instead.

Yes, it is natural and correct.

However, many Danes might also say:

• Jeg går udenfor for at få lidt frisk luft.

That means I’m going outside to get some fresh air, and it is probably even more common in everyday speech.

The difference is small:

• for at trække vejret i den friske luft = emphasizes breathing in the fresh air
• for at få lidt frisk luft = emphasizes getting some fresh air

Both are perfectly understandable and natural.

Yes, Danish word order is somewhat flexible, though some versions sound more natural than others.

Your sentence:

• Jeg går udenfor for at trække vejret i den friske luft.

is very natural.

You could also say:

• Jeg går for at trække vejret i den friske luft udenfor.

But that usually sounds less natural here, because udenfor most naturally belongs with går: the speaker is going outside.

So for this meaning, the original order is the best and most idiomatic.

English often says get some fresh air, but Danish does not always need an equivalent of some.

In your sentence, Danish simply says:

• i den friske luft = in the fresh air

And in another common version:

• få frisk luft = get fresh air

If you want to add the idea of a bit of / some, Danish can use lidt:

• få lidt frisk luft = get some fresh air

So Danish may include that extra word, but it does not have to.