Kan du bringe avisen?

Because this is a yes/no question. In Danish, yes/no questions usually put the finite verb before the subject.

Statement: Du kan bringe avisen.
Question: Kan du bringe avisen?

This is similar to English You can bring the newspaper versus Can you bring the newspaper?

Kan is the present tense of kunne, and here it means can or be able to.

In real conversation, Kan du ...? can do two jobs: it can ask about ability, and it can also function as a request, just like English Can you ...?

So depending on context, it may sound like: Are you able to bring the newspaper? or Can you bring the newspaper?

Because after a modal verb like kan, Danish uses the bare infinitive.

So you say: kan bringe

not: kan at bringe

This works like English: can bring

not: can to bring

Other common Danish modal verbs that work the same way are vil, skal, må, and bør.

Bringe means to bring or sometimes to deliver.

It is correct in this sentence. However, depending on the situation, Danish speakers might also use other verbs: tage ... med = bring ... along
hente = fetch / go get
komme med = bring along

So bringe is perfectly fine, but in some everyday situations another verb might sound more natural.

Because Danish usually adds the definite article to the end of the noun.

So: avis = newspaper
en avis = a newspaper
avisen = the newspaper

English uses a separate word, the, but Danish often uses a suffix instead.

The basic form is avis.

Its indefinite singular is en avis, so it is a common gender noun, not a neuter noun. That is why the definite singular form is avisen.

Useful forms: en avis = a newspaper
avisen = the newspaper
aviser = newspapers
aviserne = the newspapers

Yes, usually it is. Kan du ...? is a normal everyday way to ask someone to do something.

Still, tone and context matter. If you want to sound softer, Danish often adds small words or uses a slightly different verb form, for example:

Kan du lige bringe avisen?
Kunne du bringe avisen?
Vil du bringe avisen?

The word lige often makes a request sound more natural and less abrupt, even though its literal meaning does not fully match English just in every context.

A rough pronunciation guide is:

kahn doo BRING-uh ah-VEE-sen

A few helpful points: bringe has two syllables
the -e at the end is weak
avisen is stressed on the middle syllable: a-VI-sen
du is usually unstressed in normal speech

Like many Danish sentences, it is often pronounced more softly and smoothly than an English speaker might expect.