Die Unterlage liegt auf dem Schreibtisch im Büro.

• liegen = to lie (be in a horizontal position; static)
• legen = to lay (put something down; movement)
• stehen = to stand (be in a vertical position)
  Since the document is already lying flat on the desk (a static location), you choose liegt.

auf is a Wechselpräposition (two-way preposition):
• For Wo? (where) it takes the dative → dem Schreibtisch
• For Wohin? (where to) it takes the accusative → den Schreibtisch
Here we describe the location of the document (Wo liegt sie?), so we use the dative form dem.

German distinguishes between surfaces and enclosed spaces:
• auf + dative → on (surface) → auf dem Schreibtisch
• in + dative → in (inside) → im Büro
An office is viewed as an enclosed room, not a surface, so you cannot use auf with Büro here.

im is a contraction of in dem.
Since in indicates location (dative case) in this sentence, you get dem Büro, which contracts naturally to im Büro. Contractions like im, am (an dem) and beim (bei dem) are widespread in German.

Yes. German word order is flexible. You can front any element for emphasis without changing the core meaning:
• Im Büro liegt die Unterlage auf dem Schreibtisch.
• Auf dem Schreibtisch im Büro liegt die Unterlage.
Both are correct; you simply shift the focus to whichever phrase you place first.

You can use sich befinden (to be located) for a more formal tone:
Die Unterlage befindet sich auf dem Schreibtisch im Büro.
This phrasing is common in official reports or technical descriptions.

Yes, but each synonym has its own nuance:
• Dokument = a neutral document of any kind
• Akte = a file or case file (often legal)
• Mappe = a folder or binder containing papers
• Unterlage often implies a supporting document or underlay
Choose the word that best fits your specific context.

Unterlage is pronounced [ˈʊntɐˌlaːɡə]. Key points:
• Stress on the first syllable: UN-ter-la-ge
• The g before e is a hard [g] sound (as in gut)
• The a in the third syllable is long ([aː])