Jeg går ud af huset klokken halv ni, så jeg kan nå toget.

Danish often builds movement expressions in pieces:

• går = go / walk
• ud = out
• af huset = of the house / out of the house

So går ud af huset literally means goes out of the house. English often prefers a single verb like leave, but Danish very naturally uses this kind of combination. You could also say forlader huset, but that sounds a bit more formal than everyday går ud af huset.

Not necessarily in a very strict sense. At gå often does mean to walk, but in phrases like gå ud af huset it can simply mean go out / leave the house. The focus is on the action of going out, not strongly on the method of transport.

If you wanted to be more specific, Danish could use another verb:

• kører hjemmefra = leave home by car / drive away from home
• cykler hjemmefra = leave home by bike

But in your sentence, går is perfectly natural.

Because Danish usually puts the definite article at the end of the noun as a suffix.

• hus = house
• huset = the house
• tog = train
• toget = the train

This is one of the biggest structural differences from English. So instead of a separate word like the, Danish often adds -et or -en to the noun.

In Danish, the normal definite form is the ending on the noun:

• huset = the house

det hus usually means that house, not just the house. It can also appear when there is an adjective:

• det store hus = the big house

So in your sentence, huset is the normal and expected form.

Klokken literally means the clock, but in time expressions it works like at before a clock time.

So:

• klokken halv ni = at half past eight in meaning

It is a very common way to introduce a specific time. In everyday speech, Danes may sometimes just say halv ni if the context is clear, but klokken halv ni is completely normal.

This is a classic Danish time-expression issue for English speakers.

In Danish, halv ni means halfway to nine, so it is 8:30.

Compare:

• halv otte = 7:30
• halv ni = 8:30
• halv ti = 9:30

English half nine can be confusing because different English varieties use it differently, but in Danish halv ni is definitely 8:30.

Because Danish very often uses the present tense for planned, scheduled, or near-future actions.

So Jeg går ud af huset klokken halv ni is completely natural for something that will happen later. English does this too in some cases:

• I leave at 8:30 tomorrow
• The train departs at 9

Danish does not need a special future form here.

Here så means something like so that or in order that. That gives you a clause with normal subject-verb order:

• så jeg kan nå toget

If så were being used more like then/so in a new main clause, you could get:

• Så kan jeg nå toget

So the difference is about the type of clause. In your sentence, så jeg kan nå toget expresses purpose: so that I can catch the train.

At nå basically means to reach, to make it, or to get somewhere in time.

In this sentence, nå toget is best understood as:

• catch the train
• make the train
• literally, reach the train in time

So jeg kan nå toget does not mean only physically reaching the train; it means reaching it before it leaves.

Because kan is a modal verb, and modal verbs in Danish are followed by the bare infinitive.

So you get:

• jeg kan nå toget
• not jeg kan at nå toget

This is similar to English:

• I can catch the train
• not I can to catch the train

Other common Danish modal verbs work the same way:

• vil
• skal
• må
• bør

Yes. Danish often allows that. You could say:

• Klokken halv ni går jeg ud af huset, så jeg kan nå toget.

When something other than the subject comes first, Danish keeps the finite verb in second position. That is why you get:

• Klokken halv ni går jeg ...
• not Klokken halv ni jeg går ...

This is a very important Danish word-order rule.

The comma separates the first clause from the following clause of purpose/result:

• Jeg går ud af huset klokken halv ni, så jeg kan nå toget.

In practice, Danish comma use can vary a bit depending on style and comma system, but a comma here is very common and natural. For a learner, it is enough to see it as marking the boundary between the two parts of the sentence.