Min nabo er høflig, men hendes søn kan være uhøflig, hvis han er træt.

No. Nabo means neighbor and can refer to either a man or a woman.

In this sentence, we understand the neighbor is female because the next part says hendes søn = her son. So the biological sex comes from hendes, not from nabo itself.

This is a good reminder that Danish grammatical gender and real-world sex are not the same thing.

Because after a possessive like min, din, hans, hendes, and so on, Danish normally uses the base form of the noun, not the definite form.

So:

• min nabo = my neighbor
• naboen = the neighbor

You do not combine them as min naboen in normal Danish.

Because nabo is a common-gender noun in Danish.

Danish possessives change like this:

• min for common gender singular
• mit for neuter singular
• mine for plural

So:

• min nabo = my neighbor
• mit hus = my house
• mine naboer = my neighbors

This is about the difference between non-reflexive and reflexive possessives.

• hendes = her
• sin/sit/sine = his/her/its own, but only when it refers back to the subject of the same clause

Here, hendes refers to my neighbor from the earlier clause:

• Min nabo er høflig, men hendes søn ...
• My neighbor is polite, but her son ...

We use hendes because the possessor is the neighbor mentioned earlier, not the subject of the same clause in a reflexive way.

A simple contrast:

• Hun elsker sin søn = She loves her own son
• Hun elsker hendes søn = She loves her son referring to some other woman’s son

So in your sentence, hendes is the natural choice.

Because they are predicate adjectives after er and være.

In Danish, adjectives often stay in their basic form after verbs like at være.

So:

• naboen er høflig = the neighbor is polite
• sønnen kan være uhøflig = the son can be rude

If the noun were neuter singular, you would usually add -t:

• barnet er høfligt = the child is polite

And with plural or definite forms, you often use -e:

• de er høflige = they are polite

The prefix u- often works like English un-.

So:

• høflig = polite
• uhøflig = impolite / rude

It is a very common Danish pattern:

• heldig = lucky

• uheldig = unlucky

• enig = in agreement
• uenig = disagreeing

So uhøflig is not a separate random word to memorize; it follows a common word-building pattern.

Not really. Here kan være is closer to can be, may be, or can sometimes be.

So the sentence does not mean the son has the skill to be rude. It means that being rude is a possible or occasional behavior, especially under a condition:

• hvis han er træt = if he is tired

So the sense is:

• her son can be rude when he is tired
• or her son may be rude if he is tired

Because hvis introduces a subordinate clause.

In a Danish main clause, the verb is usually in second position:

• Min nabo er høflig
• Hendes søn kan være uhøflig

But after a subordinating word like hvis = if, Danish uses subordinate clause word order:

• hvis han er træt

That means the subject han comes before the verb er.

So:

• main clause: Han er træt
• subordinate clause: ..., hvis han er træt

In this particular example, the order looks the same as English, which is helpful.

The comma before men is straightforward: it separates two coordinated clauses:

• Min nabo er høflig
• men hendes søn kan være uhøflig

The comma before hvis han er træt marks the start of a subordinate clause.

Danish uses commas more systematically around subordinate clauses than English often does, so learners notice them quickly. In practice, you will often see:

• ..., hvis han er træt

So the commas help show the sentence structure clearly.

These vowels are often tricky for English speakers.

• ø in høflig and søn is a rounded front vowel.
  A rough approximation is the vowel in French deux or German schön. English does not have an exact match.

• æ in træt is more open, somewhat like the vowel in English cat, but not exactly the same.

Very rough guides:

• høflig: something like HUH-fli with rounded lips on the first vowel
• søn: roughly like sirn or surn, but with rounded lips and no exact English equivalent
• træt: roughly like tret with a more open vowel

If you are learning pronunciation, it is best to hear native audio, because Danish vowels are hard to guess accurately from English spelling comparisons alone.