Såret på min finger gør stadig ondt.

Because såret is the definite singular form of the noun sår, which means wound.

• et sår = a wound
• såret = the wound

So the sentence is talking about a specific wound, not just any wound.

Also, sår is a neuter noun, which is why its indefinite article is et.

Yes. Såret can also be the past participle/adjective form of såre, meaning hurt or wounded.

So depending on context, såret can mean:

• the wound (noun)
• hurt / wounded (adjective or participle)

In Såret på min finger gør stadig ondt, it is clearly a noun, because it is followed by på min finger and functions as the subject of the sentence.

Because finger is a common-gender noun in Danish.

In Danish:

• common gender nouns take en
• neuter nouns take et

Since it is en finger, the possessive is:

• min finger = my finger

If the noun were neuter, you would use mit instead.

Because in Danish, a possessive word like min, din, hans, hendes, and so on normally replaces the article.

So you say:

• min finger = my finger

not something like:

• den min finger

This works much like English, where my finger already includes the possessive idea and does not need the or a.

Here på is used because the wound is understood as being on the finger, usually on its surface.

• på fingeren = on the finger
• i fingeren = in the finger

If you said i fingeren, it would suggest something more internal, like pain inside the finger or something embedded in it. For a wound located on the finger, på is the natural choice.

Because gøre ondt is the normal Danish expression for to hurt / to cause pain.

Literally, gør ondt means something like does painful, but you should treat it as a fixed expression:

• Det gør ondt = It hurts
• Min arm gør ondt = My arm hurts
• Såret gør ondt = The wound hurts

So even though English often uses the single verb hurt, Danish usually uses the phrase gøre ondt.

Because in the expression gøre ondt, Danish uses the neuter form ondt.

The adjective is:

• ond = bad, evil, painful

But in this idiomatic expression, the form is always ondt:

• Det gør ondt
• Det gjorde ondt
• Gør det ondt?

So you should learn gøre ondt as a set phrase. Using ond here would sound wrong.

Because in a normal Danish main clause, the finite verb usually comes early, and adverbs like stadig often come after it.

So the structure is:

• Såret = subject
• gør = finite verb
• stadig = adverb
• ondt = part of the expression gøre ondt

That is why the sentence is:

• Såret på min finger gør stadig ondt

and not normally:

• Såret på min finger stadig gør ondt

The latter word order would only make sense in a subordinate clause, for example after at.

Because the speaker is referring to a specific, identifiable wound.

Using the definite form suggests that both speaker and listener know which wound is meant, or that it is obvious from context.

Compare:

• Et sår på min finger gør ondt = A wound on my finger hurts
  This sounds more general or less natural unless you are introducing it for the first time.

• Såret på min finger gør ondt = The wound on my finger hurts
  This points to one particular wound.

So the definite form is very natural here.

Yes, but it means something slightly different.

• Såret på min finger gør stadig ondt focuses on the wound
• Jeg har stadig ondt i fingeren focuses on pain in the finger

The second sentence is more about your physical experience of pain in the finger as a whole. The original sentence is more specific: it is the wound itself that still hurts.

So both are possible, but they are not exactly the same in focus.

Yes. Gør is the present tense of gøre.

So:

• gør = does / is doing
• in gør ondt, it gives the meaning hurts / is hurting

The word stadig adds the idea of still, so the sentence describes something that continues to be true now.