Das heruntergeladene Dokument ist auf dem Computer gespeichert.

Because Dokument is a neuter noun in German, so its article in the nominative singular is das.

• der = masculine
• die = feminine
• das = neuter

In this sentence, Dokument is the subject, so it stays in the nominative case: das Dokument.

Because it is being used like an adjective before a noun.

The basic past participle is:

• heruntergeladen = downloaded

But when a participle is placed in front of a noun, it takes an adjective ending:

• das heruntergeladene Dokument

Here, the ending is -e because:

• the noun is neuter
• it is singular
• it is in the nominative
• it follows the definite article das

This is the same pattern as with ordinary adjectives:

• das große Haus
• das gespeicherte Dokument
• das heruntergeladene Dokument

It comes from a verb, but in this sentence it is functioning as an adjective.

The verb is:

• herunterladen = to download

Its past participle is:

• heruntergeladen = downloaded

When that participle is put before a noun, German treats it like an adjective:

• das heruntergeladene Dokument = the downloaded document

So it is verb-derived, but grammatically here it behaves like an adjective.

Yes, herunterladen is a separable verb.

Its parts are:

• herunter
  • laden

In a normal main clause in the present tense, the prefix separates:

• Ich lade das Dokument herunter.

In the infinitive or past participle, it stays together:

• infinitive: herunterladen
• past participle: heruntergeladen

So in your sentence:

• heruntergeladene comes from heruntergeladen
• that comes from the verb herunterladen

Ist gespeichert literally looks like is saved/stored.

It is built from:

• ist = is
• gespeichert = saved/stored

This describes the current state of the document: it is stored on the computer.

So the sentence is not mainly focusing on the action of saving, but on the result or state after that action.

English does something similar:

• The document is saved on the computer.

Because German often places the non-finite part of the predicate at the end of the clause.

Here the predicate is:

• ist gespeichert

The conjugated verb ist goes in the second position, and the participle/adjective-like part gespeichert goes to the end:

• Das heruntergeladene Dokument ist auf dem Computer gespeichert.

This is very common in German with:

• participles
• infinitives
• separable prefixes
• multi-part verb structures

Because this sentence describes a location, not a movement toward somewhere.

German uses different cases after some prepositions depending on meaning. Auf is one of them.

• dative = location, where something is
• accusative = direction, where something is going

Here, the document is already stored on the computer, so it is a location:

• auf dem Computer

Compare:

• Das Dokument ist auf dem Computer gespeichert.
  location → dative

• Ich lade das Dokument auf den Computer.
  movement/direction → accusative

Because Computer is masculine: der Computer.

After auf with a location meaning, German uses the dative case. The dative singular form of der is dem.

So:

• nominative: der Computer
• dative: dem Computer

That gives:

• auf dem Computer

This is mostly a matter of idiomatic usage.

In German, when talking about files, programs, or data being stored on a device, auf is very common:

• auf dem Computer
• auf dem Handy
• auf der Festplatte

English often uses on in the same way:

• on the computer

You may also hear im Computer in some contexts, but auf dem Computer is the more natural choice for stored files and similar digital content.

It is very close to what learners often think of as a passive structure, but more specifically it describes a state rather than an action.

Compare these:

• Das Dokument wird gespeichert.
  The document is being saved.
  This focuses on the action/process.

• Das Dokument ist gespeichert.
  The document is saved. / The document is stored.
  This focuses on the resulting state.

So ist gespeichert is usually understood as a state/result, not an ongoing action.

Yes, you can, but it means something slightly different.

• Das heruntergeladene Dokument ist auf dem Computer gespeichert.
  The document that has been downloaded is stored on the computer.
  Here heruntergeladen describes which document you mean.

• Das Dokument ist heruntergeladen.
  The document has been downloaded.
  Here the sentence tells you the download has been completed.

So in your original sentence:

• heruntergeladene identifies the document
• gespeichert tells you its current state/location

The structure is:

• Das heruntergeladene Dokument = subject
• ist = finite verb
• auf dem Computer = prepositional phrase
• gespeichert = predicate complement / participle at the end

So the pattern is:

Subject + verb + additional information + final participle/adjective

This is a very common German word order pattern.