Han redder barnet.

Redde is the infinitive, like English to save.
Redder is the present tense, like saves or is saving.

In Danish, the present tense is usually formed by adding -r to the infinitive:

• at redde = to save
• redder = save/saves/is saving

So Han redder barnet uses the finite verb form needed in a normal sentence.

No. In Danish, the present tense form is the same for all persons:

• jeg redder = I save
• du redder = you save
• han redder = he saves
• vi redder = we save

So unlike English, Danish does not add a special -s only for he/she/it.

Because Danish usually puts the definite article on the end of the noun.

With barn:

• barn = child
• et barn = a child
• barnet = the child

So barnet is literally child + the.

Because barn is a neuter noun in Danish.

Danish singular nouns usually belong to one of two genders:

• common gender: often takes en / -en
• neuter: takes et / -et

Since it is:

• et barn = a child

the definite form becomes:

• barnet = the child

If it were a common-gender noun, the definite ending would usually be -en instead.

Normally, no.

A singular countable noun in Danish usually needs some kind of determiner, just as in English. So you would normally say either:

• Han redder et barn = He saves a child
• Han redder barnet = He saves the child

The bare singular barn by itself is not the normal choice here.

Barnet is the normal definite form meaning the child.

Det barn is more like that child or that particular child, often with extra emphasis, contrast, or pointing.

For example:

• Han redder barnet = He saves the child
• Han redder det barn = He saves that child / that particular child

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

• det lille barn = the small child

So barnet is the ordinary definite form, while det barn is more specific or contrastive.

This is the normal word order for a main clause: subject + verb + object.

• Han = subject
• redder = verb
• barnet = object

Danish also follows the V2 rule in main clauses, which means the finite verb is in the second position. In this sentence, the subject comes first, so the verb naturally comes second:

• Han redder barnet

If something else comes first, the verb still stays second:

• Nu redder han barnet = Now he is saving the child

It can mean both, depending on context.

The Danish present tense often covers both:

• He saves the child
• He is saving the child

So Han redder barnet could describe:

• something happening right now
• a general or repeated action
• sometimes even a near-future action, depending on context

Danish does not require a separate form exactly like English is saving in every case.

A rough pronunciation is:

han REH-thur BAR-nuhth

A more IPA-style version is approximately:

[han ˈʁɛðɐ ˈbɑːnəð]

A few useful pronunciation notes:

• redder has a soft Danish d, not a strong English d
• the ending -et in barnet is often pronounced something like -eð
• the Danish r is very different from the English r

So the written form is straightforward, but the sounds are more Danish than an English spelling guide can fully show.