Die Schätzfrage steht auf dem Antwortbogen.

Because Schätzfrage is a feminine noun in German. The article die is the nominative singular feminine form of the.

A useful rule here is that in many German compound nouns, the last part determines the grammatical gender.

• die Frage = the question
• so die Schätzfrage is also feminine

Even though schätzen means to estimate / to guess, the gender comes from Frage, not from the verb.

Schätzfrage is a compound noun:

• schätzen = to estimate, to guess
• die Frage = question

So Schätzfrage means something like estimate question, guessing question, or tie-breaker estimation question, depending on context.

It is the kind of question where you do not need an exact known fact from memory, but instead make an estimate, such as How many jellybeans are in the jar?

In German, stehen often means more than just to stand physically. It is also commonly used to mean that something is written, printed, or located in a written place.

So:

• Die Schätzfrage steht auf dem Antwortbogen.
  = The estimation question appears / is written on the answer sheet.

German often uses verbs like these in a broader way:

• stehen = stand, be written
• liegen = lie, be located
• hängen = hang, be posted

Using ist would be less natural here if the idea is that the question is printed on the sheet.

Because auf is a two-way preposition, which means it can take either:

• dative for location
• accusative for movement toward a destination

Here, the sentence describes where the question is located, not motion. So German uses the dative:

• auf dem Antwortbogen = on the answer sheet

Compare:

• Die Schätzfrage steht auf dem Antwortbogen.
  The question is on the sheet. → location → dative

• Ich schreibe die Schätzfrage auf den Antwortbogen.
  I write the question onto the sheet. → movement/direction → accusative

Antwortbogen is a masculine noun:

• nominative: der Antwortbogen
• dative: dem Antwortbogen

Since auf here expresses location, it requires the dative case, so der changes to dem.

This is a standard article change:

• der → dem in the dative singular masculine
• das → dem in the dative singular neuter
• die → der in the dative singular feminine

Antwortbogen is another compound noun:

• die Antwort = answer
• der Bogen = sheet, form, page

So der Antwortbogen means answer sheet or response form, depending on context.

Again, the last part determines the gender:

• der Bogen is masculine
• therefore der Antwortbogen is masculine

German main clauses usually follow the V2 rule, which means the finite verb comes in the second position.

In this sentence:

• Die Schätzfrage = position 1
• steht = position 2
• auf dem Antwortbogen = the rest

So the structure is perfectly normal for a German statement:

• Subject + verb + other elements

You could also move another element to the front, but the verb would still stay second:

• Auf dem Antwortbogen steht die Schätzfrage.

That version is also correct; it just emphasizes the location more.

Yes, it is the same verb form historically, but in this context it clearly comes from the meaning to estimate or to guess.

The verb schätzen can mean:

• to estimate
• to value
• to appreciate

In Schätzfrage, the intended meaning is definitely estimate. So this is not a question about appreciation; it is a question where you give an estimated answer.

Yes, it would probably be understood, but steht auf dem Antwortbogen sounds more natural if you mean the question is written there.

The difference is roughly:

• ist auf dem Antwortbogen = is on the answer sheet
• steht auf dem Antwortbogen = is written on the answer sheet

German often prefers stehen for text appearing on paper, signs, websites, labels, and so on.

A natural pronunciation would stress the important content words:

Die SCHÄTZfrage steht auf dem ANTwortbogen.

A few pronunciation notes:

• ä in Schätz- sounds somewhat like the e in British English bed, though not exactly the same
• sch is like sh
• z in German is pronounced ts
• w in German sounds like English v
• bogen has a long o sound: BOH-gen

A rough English-style approximation is:

dee SHETS-frah-guh shtayt owf daym ANTVORT-boh-gen

That is only an approximation, but it may help at first.

Yes. German allows some flexibility, especially in main clauses, as long as the finite verb stays in second position.

For example:

• Die Schätzfrage steht auf dem Antwortbogen.
  Neutral word order

• Auf dem Antwortbogen steht die Schätzfrage.
  Emphasizes on the answer sheet

Both are correct. The choice depends on what the speaker wants to highlight.

Because German very commonly forms compound nouns by joining words together into a single word.

So instead of writing:

• Schätz Frage
• Antwort Bogen

German writes:

• Schätzfrage
• Antwortbogen

This is completely standard. English often writes similar ideas as separate words, but German usually combines them. The last element is the main noun, and the earlier part modifies it.