Die Spielfigur steht auf dem Spielplan.

Spielfigur is a feminine noun, so its definite article in the nominative singular is die.

A useful extra point: in German compound nouns, the last part usually determines the gender.
Here, the last part is Figur, and die Figur is feminine, so the whole word is also feminine:

• die Figur
• die Spielfigur

Yes. German very often combines nouns into compound words.

• Spiel = game
• Figur = figure / piece / character

So Spielfigur is a single word meaning something like game piece or playing piece, depending on context.

Because auf can take different cases, and here it is followed by the dative.

The basic noun is:

• der Spielplan = the board / game board

But after auf when it describes a location rather than movement, German uses the dative:

• auf dem Spielplan = on the game board

So:

• nominative: der Spielplan
• dative: dem Spielplan

Because the sentence describes where something is, not where it is going.

German makes an important distinction with prepositions like auf:

• dative = location, position
• accusative = direction, movement toward somewhere

So:

• Die Spielfigur steht auf dem Spielplan. = The piece is on the board.
  
  • location → dative
• Die Spielfigur kommt auf den Spielplan. = The piece goes onto the board.
  
  • movement → accusative

This is a very common German pattern.

German often prefers a more specific position verb where English might just say is.

Here, stehen literally means to stand, but it is also used for things that are in an upright or set position. A game piece is often thought of as standing on the board, so steht sounds natural.

Compare:

• steht = is standing / is positioned standing
• liegt = is lying
• ist = is

So Die Spielfigur steht auf dem Spielplan is more natural than using ist in this context.

Usually not if you mean a normal game piece in its usual position.

• steht is used when the object is thought of as upright
• liegt is used when something is lying flat or has fallen over

So if the piece is where it normally is on the board, steht is the normal choice. If it has tipped over, then liegt might make sense.

Because German main clauses normally follow the V2 rule: the finite verb comes in the second position.

In this sentence:

• Die Spielfigur = first element
• steht = second element
• auf dem Spielplan = the rest

So the structure is perfectly normal for German.

You can also move another element to the front, but the verb still stays second:

• Auf dem Spielplan steht die Spielfigur.

Spielplan is masculine:

• der Spielplan = the game board / board layout

Its plural is:

• die Spielpläne

That is why the dative singular form in the sentence is dem Spielplan.

Here die is the feminine singular definite article, and it is pronounced dee.

A helpful pronunciation point: ie in German is usually pronounced like a long ee sound.

So:

• die → dee
• Spiel → roughly shpeel

This is different from English spelling habits, so it is worth remembering.

Here it is definitely the article the.

German die can sometimes mean different things:

• die Frau = the woman
• sie = she
• sie = they

But in this sentence, die comes directly before a noun, Spielfigur, so it is the definite article:

• die Spielfigur = the game piece