Min nabo er flink mod børnene.

Because min already makes the noun definite.

In Danish, possessives such as min, din, hans, hendes, vores, and deres normally replace the article/definite ending.

• en nabo = a neighbor
• naboen = the neighbor
• min nabo = my neighbor

So min naboen is not correct.

Nabo is a common gender noun, so its basic form is en nabo.

Its forms are:

• en nabo = a neighbor
• naboen = the neighbor
• naboer = neighbors
• naboerne = the neighbors

You often just have to learn the gender with the noun, but dictionaries will show it.

Er is the present tense of at være = to be.

So:

• jeg er = I am
• du er = you are
• han/hun er = he/she is
• min nabo er = my neighbor is

Danish verbs do not change according to person the way English does. The present tense form is the same for all subjects.

Here flink means something like kind, nice, or good-hearted in the way someone behaves toward others.

That said, flink can have a few shades of meaning depending on context:

• flink mod nogen = kind/nice to someone
• et flinkt barn = a well-behaved/nice child
• han er flink til dansk = he is good at Danish

So flink is a flexible word. In this sentence, because it is followed by mod børnene, it clearly means kind to.

Because flink mod nogen is a common Danish pattern meaning kind/nice toward someone.

Here mod means toward(s) in the sense of attitude or behavior.

So:

• flink mod børnene = kind to the children
• flink mod sin mor = kind to his/her mother

You cannot freely replace mod with any other preposition here.

They are similar, but not identical.

• flink mod børnene focuses on how the person treats the children

  • kind, nice, gentle, considerate toward them

• god med børn focuses more on being good with children

  • able to handle them well
  • naturally good around them
  • often good at interacting with them

So min nabo er flink mod børnene emphasizes kindness toward the children, not necessarily skill in dealing with children in general.

Børnene is the definite plural form: the children.

The noun is irregular:

• et barn = a child
• barnet = the child
• børn = children
• børnene = the children

So the sentence is talking about specific children, not children in general.

Compare:

• flink mod børn = kind to children / good with children in general
• flink mod børnene = kind to the children

Because the subject is singular and common gender: min nabo.

When an adjective is used after er as a predicate adjective, it often agrees with the subject:

• min nabo er flink
• mine naboer er flinke
• huset er stort

Here the subject is singular common gender, so the basic form flink is used.

It is the normal Danish main-clause order.

• Min nabo = subject
• er = finite verb
• flink mod børnene = rest of the sentence

Danish is a verb-second language, which means the finite verb usually comes in the second position in main clauses. In this sentence, the subject phrase Min nabo is the first element, so er comes second.

For example:

• Min nabo er flink mod børnene.
• I dag er min nabo flink mod børnene.

In both cases, the finite verb er stays in second position.

Yes, but it is slightly different in tone.

• flink mod børnene = kind/nice in behavior toward the children
• sød mod børnene = sweet/lovely toward the children

Flink often sounds a bit more neutral and practical.
Sød sounds warmer and more affectionate.

So both can work, but flink is a very natural choice if you simply want to describe considerate behavior.