Præsidenten læser avisen.

Because in Danish, the definite article the is usually added to the end of the noun instead of written as a separate word.

• præsident = president

• præsidenten = the president

• avis = newspaper
• avisen = the newspaper

So Danish often says the equivalent of president-the and newspaper-the.

In Danish, singular definite nouns usually take a suffix:

• common gender nouns: -en
• neuter nouns: -et

So instead of a separate article before the noun, Danish normally attaches it:

• en avis = a newspaper

• avisen = the newspaper

• en præsident = a president
• præsidenten = the president

English uses a separate word; Danish often uses an ending.

The basic forms are:

• præsident = president
• læse = to read
• avis = newspaper

In the sentence:

• præsidenten is the definite singular form of præsident
• læser is the present tense of læse
• avisen is the definite singular form of avis

Læse is the infinitive, meaning to read.
Læser is the present tense, meaning read / reads / is reading, depending on context.

A very common pattern in Danish is:

• infinitive: læse
• present tense: læser

So:

• jeg læser = I read / I am reading
• du læser = you read / you are reading
• præsidenten læser = the president reads / is reading

No. Danish verbs do not change for person in the present tense.

So you get:

• jeg læser = I read
• du læser = you read
• han læser = he reads
• vi læser = we read

The verb form stays the same. This is simpler than English.

It can mean either, depending on context.

Danish present tense often covers both:

• The president reads the newspaper
• The president is reading the newspaper

If no extra context is given, English may translate it either way.

This is the normal basic word order for a simple statement:

Subject + Verb + Object

• Præsidenten = subject
• læser = verb
• avisen = object

So it works just like standard English word order here: The president reads the newspaper.

Not always. Danish is a V2 language, which means the finite verb is usually in the second position in main clauses.

This sentence has the normal order:

• Præsidenten læser avisen

But if something else comes first, the verb still stays second:

• I dag læser præsidenten avisen = Today, the president is reading the newspaper

So the word order can move around more than in English, but the verb still tends to stay in position two.

Because præsident and avis are common gender nouns in Danish.

Danish has two grammatical genders:

• common gender
• neuter

Common gender nouns usually take:

• indefinite article: en
• definite ending: -en

So:

• en præsident → præsidenten
• en avis → avisen

If a noun were neuter, it would usually take:

• indefinite article: et
• definite ending: -et

The letter æ is a very common Danish vowel. For English speakers, it is often somewhat like the vowel in cat, but the exact sound depends on the word and speaker.

Roughly:

• præsidenten sounds approximately like preh-see-DEN-dən
• læser sounds approximately like LEH-ser

A few notes:

• Danish pronunciation is often softer and less clearly pronounced than spelling suggests.
• The final -er in læser is not usually pronounced like strong English er.
• The final -en in præsidenten is also reduced.

These English-style approximations are only rough guides.

Normally, no.

If the noun is definite by itself, Danish usually uses the suffix only:

• præsidenten
• avisen

Using both a separate definite article and the definite ending is usually wrong in a simple phrase.

However, when there is an adjective, Danish often uses both a separate article and a definite ending pattern:

• den nye avis = the new newspaper
• den amerikanske præsident = the American president

So in your sentence, with no adjective, præsidenten and avisen are correct on their own.

It would be:

En præsident læser en avis.

That means:

• en præsident = a president
• en avis = a newspaper

So the difference is:

• Præsidenten læser avisen = definite nouns
• En præsident læser en avis = indefinite nouns

Usually yes: it means the newspaper, so it refers to a specific newspaper that is known from the situation or context.

In real use, that could mean:

• the newspaper the president is holding
• the usual newspaper someone reads
• a newspaper already mentioned before

So the definite form usually points to something identifiable, just like the newspaper in English.