Kartta näyttää, missä aarre on.

Because missä aarre on is a subordinate clause: it adds the content of what the map shows.

Finnish normally puts a comma before a subordinate clause, so:

• Kartta näyttää, missä aarre on.

This is very standard Finnish punctuation.

Missä means where in the sense of in what place.

It is the inessive form of mikä / mikä?’s location series, and it is used for location inside / in something, or more generally at a place.

Here it introduces an indirect question:

• missä aarre on = where the treasure is

So it is not asking a direct question by itself; it is embedded inside the larger sentence.

In Finnish subordinate clauses, the word order is often more statement-like than in direct questions.

Compare:

• Direct question: Missä aarre on? = Where is the treasure?
• Embedded clause: Kartta näyttää, missä aarre on. = The map shows where the treasure is.

So missä comes first, and then the rest of the clause follows in a normal order. English does something similar:

• direct question: Where is the treasure?
• embedded question: ...where the treasure is

It is possible in some contexts, but missä aarre on is the more neutral and expected version here.

Why?

• missä aarre on presents aarre as the known thing whose location is being shown.
• missä on aarre can sound more like the sentence is presenting the existence of a treasure at some location, or it may sound less neutral in this context.

For a learner, missä aarre on is the safest and most standard choice.

Finnish has no articles, so there is no separate word for a or the.

So:

• aarre can mean a treasure or the treasure

You understand which one it means from context. In this sentence, the context makes it clear that it means the treasure.

Kartta is in the nominative singular, which is the basic dictionary form.

Here it is the subject of the sentence:

• Kartta = the map
• näyttää = shows

So Kartta näyttää means The map shows.

Näyttää is the 3rd person singular present tense of the verb näyttää.

Here it agrees with the singular subject kartta:

• kartta näyttää = the map shows

Be aware that näyttää can have more than one meaning in Finnish, for example:

• show
• look / seem

In this sentence it clearly means show.

It functions as the content of what is being shown. In practical learner terms, yes: it behaves like the thing that näyttää points to.

You can think of the sentence structure like this:

• Kartta näyttää = The map shows
• missä aarre on = where the treasure is

So the whole clause works as the complement of näyttää.

Because missä already introduces the subordinate clause.

Finnish uses different words for different kinds of subordinate clauses:

• että = that
• missä = where
• kun = when
• miksi = why

So:

• Kartta näyttää, että aarre on täällä. = The map shows that the treasure is here.
• Kartta näyttää, missä aarre on. = The map shows where the treasure is.

You do not use että together with missä here.

Yes. Missä aarre on is an indirect question or embedded question.

Compare:

• Direct: Missä aarre on? = Where is the treasure?
• Indirect: Kartta näyttää, missä aarre on. = The map shows where the treasure is.

Finnish uses the same question word missä, but the clause is embedded inside a larger sentence.

You would change the verb inside the subordinate clause:

• Kartta näyttää, missä aarre oli.

Here:

• on = is
• oli = was

The main verb näyttää stays the same if you still mean shows.

Finnish has several location words, and they depend on the type of location:

• missä = where, in/at what place
• mihin = where to
• mistä = where from

Here the idea is static location:

• where the treasure is

So missä is correct.

If the meaning were movement, you would use something else:

• Kartta näyttää, mihin aarre vietiin. = The map shows where the treasure was taken.
• Kartta näyttää, mistä aarre löydettiin. = The map shows where the treasure was found from / where it was discovered.

To some extent, yes, but the given version is the most natural neutral order.

Neutral order:

• Kartta näyttää, missä aarre on.

You can move words around in Finnish for emphasis, but that changes the feel of the sentence. For learners, it is best to treat this sentence as a standard model:

• main clause first: Kartta näyttää
• subordinate clause after the comma: missä aarre on

That will sound natural and correct.