Sparen står på scoretavlen.

Because Danish usually marks the by adding it to the end of the noun.

• en spare = a spare
• sparen = the spare

For many en-words that end in -e, the definite ending is just -n, so:

• spare + n = sparen

This is one of the biggest differences from English, where the is a separate word.

For the same reason: Danish normally uses a suffix for the definite form.

• en scoretavle = a scoreboard
• scoretavlen = the scoreboard

You usually do not use den with a bare noun like this. Den is commonly used when there is an adjective or some extra specification:

• den store scoretavle = the big scoreboard

So in this sentence, scoretavlen by itself is the normal form.

Literally, yes: stå means stand. But in Danish, stå på often means be written on, be shown on, or appear on something like a board, sign, screen, or list.

So here står på scoretavlen is idiomatic Danish for something like:

• is shown on the scoreboard
• appears on the scoreboard

This is a very common use of stå in Danish.

Because Danish often prefers stå when something is displayed or written somewhere.

Compare:

• Det står på tavlen. = It is written on the board.
• Der står 2-1 på skærmen. = It says 2–1 on the screen.

English often uses is, shows, or says, but Danish frequently uses stå in these cases. So står sounds more natural than er here.

Står is the present tense of stå.

• infinitive: stå = to stand
• present: står = stands / is standing / is shown

In this sentence, the present tense describes the current state: the thing is currently shown on the scoreboard.

Yes. This is the normal Danish main-clause order:

• Sparen = subject
• står = verb
• på scoretavlen = prepositional phrase

So it follows the basic pattern:

Subject + Verb + other information

You could also move the location to the front for emphasis:

• På scoretavlen står sparen.

In that version, the verb still stays in second position, which is a key rule in Danish main clauses.

Because Danish normally writes compound nouns as one word.

• score + tavle = scoretavle

English often writes similar expressions as two words, but Danish usually combines them. This is very common:

• fodboldkamp
• togstation
• sommerferie

So scoretavle is exactly what you would expect in Danish spelling.

Both spare and scoretavle are common gender nouns, also called en-words.

That is why their indefinite forms take en:

• en spare
• en scoretavle

And their definite singular forms become:

• sparen
• scoretavlen

Knowing whether a noun is an en-word or an et-word is important in Danish, because it affects articles and adjective forms.

You probably could be understood, but står på scoretavlen is more idiomatic if you mean that it is displayed there.

• er på can sound more general: is on
• står på specifically fits things that are written, shown, or listed

So a learner should remember that Danish often uses stå where English would simply use be.

Yes. På is the normal choice with things like boards, signs, screens, lists, and tables when something appears on them.

Examples:

• på tavlen = on the board
• på skærmen = on the screen
• på listen = on the list

So på scoretavlen is exactly what you would expect.