Hun hjælper den stakkels hund.

Hjælper is the present tense of hjælpe (to help).

So:

• at hjælpe = to help
• hjælper = help / helps

In this sentence, Hun hjælper den stakkels hund, it means she helps the poor dog.

A useful point for English speakers: Danish verbs do not change for person the way English does. So the same present-tense form is used with I, you, he, she, we, they:

• jeg hjælper
• du hjælper
• hun hjælper
• vi hjælper

Den here is the definite article meaning the for a common-gender noun.

So:

• en hund = a dog
• den ... hund = the ... dog

Because the noun is being described by an adjective-like word (stakkels), Danish uses a separate word for the before the description:

• den stakkels hund = the poor dog

Because hund is a common-gender noun in Danish.

You learn the gender with the indefinite article:

• en hund = a dog → common gender
• et hus = a house → neuter

For definite phrases with an adjective, the article matches the gender:

• den store hund = the big dog
• det store hus = the big house

So here it must be den, because hund is an en-word.

Because in standard Danish, when a noun is definite and has a modifier in front of it, you normally use the separate definite article and keep the noun in its basic form.

Compare:

• hunden = the dog
• den stakkels hund = the poor dog

So:

• without a modifier: hunden
• with a modifier: den stakkels hund

This is a very important pattern in Danish.

Here it is an article, not a pronoun.

It is part of the noun phrase:

• den stakkels hund = the poor dog

So den is not standing alone as it/that. It is just functioning as the.

Because stakkels is normally a fixed form. It does not behave like many regular adjectives.

For example, many Danish adjectives change depending on gender/number/definiteness:

• en stor hund
• et stort hus
• de store hunde

But stakkels usually stays stakkels:

• den stakkels hund
• det stakkels barn
• de stakkels mennesker

So you can think of stakkels as a special adjective-like word that usually does not inflect.

Usually no.

In this sentence, stakkels means something like:

• poor
• pitiful
• unfortunate
• poor thing

So den stakkels hund means the dog is unfortunate, suffering, or someone feels sympathy for it.

If you want poor in the financial sense, Danish more often uses fattig.

Yes, but the basic version here is the normal, neutral order:

• Hun hjælper den stakkels hund.

That is:

• subject: Hun
• verb: hjælper
• object: den stakkels hund

Danish main clauses follow the verb-second rule, so if something else comes first, the verb still stays in second position:

• I dag hjælper hun den stakkels hund. = Today she helps the poor dog.

So the sentence can change, but the verb placement is very important.