Hvis jeg mister min pung, tager jeg ikke metroen, men går hjem fra busstoppestedet.

Because Danish main clauses normally follow the V2 rule: the finite verb comes in the second position.

Here, the whole Hvis jeg mister min pung clause comes first. That means the main clause has to begin with the verb:

• Hvis jeg mister min pung, tager jeg ikke metroen ...

If you said the main clause by itself, it would be:

• Jeg tager ikke metroen.

So the fronted if-clause causes the inversion.

Yes, but Danish often uses the present tense for real or possible future conditions, just like English does in sentences such as:

• If I lose my wallet, ...

Not:

• If I will lose my wallet, ...

So Hvis jeg mister min pung is the normal way to say this.

Because pung is a common-gender noun in Danish:

• en pung = a wallet

For possessives, Danish uses:

• min with common-gender singular nouns
• mit with neuter singular nouns
• mine with plurals

So:

• min pung
• mit hus
• mine bøger

Those endings are the Danish way of marking the definite form—the equivalent of the in English.

• en metro → metroen = the metro
• et busstoppested → busstoppestedet = the bus stop

Danish usually adds definiteness to the end of the noun instead of using a separate word like the.

Because the second part shares the same subject as the first part.

The structure is basically:

• tager jeg ikke metroen
• men går hjem fra busstoppestedet

The subject jeg is understood in the second part, so it does not have to be repeated.

This is similar to English:

• I don’t take the metro, but walk home ...

You could repeat jeg, but then it would sound more explicit or contrastive:

• ..., men jeg går hjem fra busstoppestedet.

Because hjem usually expresses movement toward home, while hjemme expresses location at home.

So:

• Jeg går hjem. = I’m going/walking home.
• Jeg er hjemme. = I’m at home.

In this sentence, the person is moving toward home, so hjem is correct.

It means from the bus stop.

• fra = from
• busstoppestedet = the bus stop

So the idea is that the person starts at the bus stop and walks home from there.

If it meant to the bus stop, Danish would use til instead:

• til busstoppestedet = to the bus stop

Because Hvis jeg mister min pung is a subordinate clause placed before the main clause, and Danish puts a comma at the boundary between them:

• Hvis jeg mister min pung, tager jeg ikke metroen ...

So in this sentence, the comma is standard and expected.

Because tage is a very common verb for using transport in Danish.

For example:

• tage bussen = take the bus
• tage toget = take the train
• tage metroen = take the metro

So this works much like English take.

You may also hear other expressions, such as køre med metroen, but tage metroen is very normal.

Because Danish, like German, usually writes compound nouns as one word.

So busstoppestedet is built from smaller parts:

• bus
• stop
• sted
• -et (definite ending)

Together, it becomes busstoppestedet.

This is very typical in Danish, and learners often need time to get used to these long compound words.