Der står en taxa foran udgangen, og chaufføren læser et kort.

Yes. In Der står en taxa foran udgangen, der means there in the sense of there is / there are.

Danish often uses der at the start of a sentence to introduce something's existence or presence:

• Der er en mand udenfor. = There is a man outside.
• Der står en taxa foran udgangen. = There is a taxi standing in front of the exit.

Here, står is used instead of er because Danish often prefers a more specific verb showing position:

• stå = stand
• ligge = lie
• sidde = sit

So the sentence is very naturally saying something like:

• There is a taxi standing in front of the exit

not just a plain There is a taxi.

Because Danish often describes where something is by using a position verb instead of just to be.

Common position verbs are:

• stå = stand
• ligge = lie
• sidde = sit

A taxa is thought of as something upright and resting on its wheels, so Danish says it stands:

• Taxaen står foran udgangen.

This is more idiomatic than Taxaen er foran udgangen, although er is not impossible in all contexts. Danish just prefers the more concrete verb.

English sometimes does this too, but less consistently:

• The bottle is on the table
• Danish would often say Flasken står på bordet

Because Danish nouns have two grammatical genders:

• common gender → takes en
• neuter gender → takes et

So:

• en taxa = a taxi
• et kort = a map / a card

Unfortunately, gender usually has to be learned with each noun.

In this sentence:

• taxa is a common-gender noun
• kort is a neuter noun

That also affects the definite form:

• en taxa → taxaen = the taxi
• et kort → kortet = the map / the card

Because Danish normally makes nouns definite by adding an ending to the noun.

So:

• en udgang = an exit
• udgangen = the exit

and

• en chauffør = a driver
• chaufføren = the driver

This is one of the biggest differences from English. Instead of putting the before the noun, Danish usually attaches definiteness to the end.

So:

• chaufføren læser et kort = the driver is reading a map

Using den is possible in some situations, but usually only when there is also an adjective or some special emphasis:

• den store taxa = the big taxi

Without an adjective, plain taxaen is the normal form.

Actually, udgangen already means the exit. The -en ending is the definite article.

So:

• foran udgangen = in front of the exit

This is completely normal Danish structure:

• preposition + definite noun with suffix

Examples:

• ved døren = by the door
• bag huset = behind the house
• foran bilen = in front of the car

You do not add an extra word meaning the in front of udgangen here.

Foran means in front of.

So:

• foran udgangen = in front of the exit

Related words:

• bag = behind
• ved siden af = beside / next to
• overfor = opposite
• i = in
• på = on

A useful contrast:

• foran refers to position in front of something
• før means before in time

So:

• foran udgangen = in front of the exit
• før klokken otte = before eight o'clock

Because Danish is a V2 language, which means the finite verb usually comes in the second position in main clauses.

In Der står en taxa foran udgangen:

1. Der = first element
2. står = verb in second position
3. en taxa = subject-like noun phrase being introduced

This is normal Danish structure.

You can also see V2 in other sentences:

• Nu kommer bussen. = Now the bus is coming.
• I dag læser chaufføren et kort. = Today the driver is reading a map.

No matter what comes first, the finite verb tends to stay in second position in a main clause.

Because og joins two main clauses, and each main clause keeps normal main-clause word order.

So the sentence is really:

• Der står en taxa foran udgangen
• og chaufføren læser et kort

In the second clause:

• chaufføren = subject
• læser = verb
• et kort = object

This is ordinary Danish word order.

Compare that with a subordinate clause, where the word order changes:

• ..., fordi chaufføren læser et kort
  Here it still looks similar because there is no adverb, but with an adverb you can see the difference more clearly:

Main clause:

• Chaufføren læser ikke et kort.

Subordinate clause:

• ..., fordi chaufføren ikke læser et kort.

So after og, you usually have normal main-clause order.

It can mean either in Danish, depending on context.

• et kort can mean a map
• et kort can also mean a card

In this sentence, since the driver is apparently trying to find a location, the meaning is almost certainly a map.

This is very common in Danish: one word can cover meanings that English separates.

Examples:

• et landkort = a geographical map
• et kreditkort = a credit card

So kort by itself is broad, and context tells you which meaning is intended.

Both are present tense.

• står = stands / is standing
• læser = reads / is reading

Danish present tense is usually formed with -r:

• stå → står
• læse → læser

Very importantly, Danish present tense often covers both:

• simple present
• present progressive

So:

• chaufføren læser et kort can mean
  the driver reads a map or, more naturally here, the driver is reading a map

Context tells you which English translation sounds best.

Because Danish usually does not need a separate progressive form like English is reading.

English often distinguishes:

• reads
• is reading

Danish usually just uses the present tense:

• læser

So:

• chaufføren læser et kort = the driver reads a map / is reading a map

If you want to emphasize an ongoing action, Danish can sometimes use expressions like:

• er ved at læse = is in the process of reading

But in ordinary sentences, the simple present is enough.

Then you would probably use definite forms:

• Taxaen står foran udgangen, og chaufføren læser et kort.

That means:

• The taxi is in front of the exit, and the driver is reading a map.

The original sentence starts with Der står en taxa..., which introduces the taxi as new information:

• There is a taxi...

So there is a difference in focus:

• Der står en taxa... = introducing a taxi into the scene
• Taxaen står... = talking about a taxi already known or identifiable

A few useful pronunciation points:

• chaufføren contains ø, a rounded vowel that does not exist in standard English. It is somewhat like the vowel in French peu or German schön, but not exactly.
• læser has æ, which sounds somewhat like the vowel in English cat, though again not exactly the same.
• The final -r in Danish is often weaker than English learners expect.

Very rough guides:

• chaufføren ≈ sho-FUR-en or shaw-FUR-en, but with a Danish ø sound
• læser ≈ LEH-ser, with æ rather open

Also, Danish pronunciation is often less phonetic than spelling suggests, so it is best to hear native audio if possible.

Yes, in modern Danish many people also say taxi. Both exist, but taxa is a well-established standard Danish form.

So you may see or hear:

• en taxa
• en taxi

The rest of the grammar works the same way. For example:

• taxaen
• taxien

If your course or dictionary uses taxa, it is a good idea to learn that form, but do not be surprised if taxi appears in real life too.