Læreren beder os markere de vigtigste ord og understrege de svære sætninger.

Because -en is the definite article attached to the noun.

• lærer = teacher
• læreren = the teacher

Danish often puts the at the end of the noun instead of using a separate word the way English does.

Beder is the present tense form of the verb at bede.

• at bede = to ask / to request
• beder = asks / is asking

So in this sentence:

• Læreren beder os ... = The teacher asks us ...

Danish present tense verbs often end in -r.

Because os is the object form of the pronoun, while vi is the subject form.

• vi = we
• os = us

Here, the teacher is asking us, so Danish uses os.

Compare:

• Vi læser. = We are reading.
• Læreren hjælper os. = The teacher helps us.

After verbs like bede in this kind of structure, Danish often uses the infinitive without at.

So:

• Læreren beder os markere ... not
• Læreren beder os at markere ...

This is similar to English patterns like ask someone do something, except English usually requires to: ask someone to mark. Danish does not use at here.

A useful pattern is:

• bede nogen gøre noget = ask someone to do something

So:

• beder os markere
• beder os understrege

are both normal.

Because the pattern is:

• bede + someone + infinitive

So the structure is:

• Læreren = subject
• beder = verb
• os = object
• markere / understrege = infinitives telling what we are asked to do

In other words, os belongs with beder, and markere tells the action we are supposed to perform.

Because both infinitives are connected to the same object os.

So the sentence means:

• the teacher asks us to mark
• and to underline

Danish avoids repeating os because it is already understood.

A fuller but less natural version would be something like:

• Læreren beder os markere de vigtigste ord og (os) understrege de svære sætninger.

The second os is unnecessary.

Because in Danish, when a plural noun phrase is definite, you usually use:

• de + adjective + noun

So:

• de vigtigste ord = the most important words
• de svære sætninger = the difficult sentences

This is different from English, where the article and adjective system works differently.

Without de, vigtigste ord would sound incomplete in this sentence.

Vigtigste is the superlative form of vigtig.

• vigtig = important
• vigtigere = more important
• vigtigst = most important
• vigtigste = the form often used before a noun in a definite phrase

So:

• de vigtigste ord = the most important words

The -e appears because it is being used attributively before the noun in a definite phrase.

Because the adjective is describing a plural definite noun phrase:

• de svære sætninger

In Danish, adjectives often take -e in definite and plural contexts.

Compare:

• en svær sætning = a difficult sentence
• svære sætninger = difficult sentences
• de svære sætninger = the difficult sentences

So svære matches the plural/definite phrase.

Because ord is one of those Danish nouns whose singular and plural indefinite forms are the same.

• et ord = a word
• ord = words

So in the phrase:

• de vigtigste ord

the noun stays ord, even though it is plural.

This is normal for some Danish nouns, especially neuter ones.

Because sætning forms its plural with -er.

• en sætning = a sentence
• sætninger = sentences

So:

• de svære sætninger = the difficult sentences

Unlike ord, this noun does show a separate plural ending.

The basic structure is:

• Læreren = subject
• beder = finite verb
• os = object
• markere ... og understrege ... = infinitive phrases

So the pattern is:

• Subject + verb + object + infinitives

This is normal Danish main-clause word order.

Also, Danish is a V2 language, which means the finite verb usually comes in the second position in main clauses. Since the sentence starts with the subject Læreren, the verb beder comes right after it.

Yes. At bede can mean both, depending on context.

• Jeg beder dig om hjælp. = I ask you for help.
• Jeg beder til Gud. = I pray to God.

In your sentence, because it has the pattern beder os + infinitive, the meaning is clearly asks us to.

Yes. Og simply links the two actions:

• markere
• understrege

So the teacher asks for two things:

1. mark the most important words
2. underline the difficult sentences

This is completely straightforward Danish coordination.

In this sentence, understrege without at is the normal choice.

Because it depends on beder os, the infinitive stays bare:

• beder os markere ... og understrege ...

Using at here would sound unnatural in standard Danish.

So a good pattern to remember is:

• bede nogen gøre noget

not

• bede nogen at gøre noget

A natural grouping is:

• Læreren beder os
• markere de vigtigste ord
• og understrege de svære sætninger

That helps show the grammar clearly:

1. the main clause: Læreren beder os
2. first requested action: markere de vigtigste ord
3. second requested action: og understrege de svære sætninger

This is often a useful way to read longer Danish sentences.