Оригинал документа уже готов.

In Russian, the verb to be is usually omitted in the present tense.

So where English says:

• The original document is ready

Russian simply says:

• Оригинал документа уже готов.

This is completely normal.
If you wanted the past or future, then forms of быть would appear:

• Оригинал документа уже был готов. — The original document was already ready.
• Оригинал документа уже будет готов. — The original document will already be ready.

So in the present tense, no separate word for is is needed.

Документа is the genitive singular of документ.

Here, the genitive shows a relationship like of the document. So:

• оригинал документа = the original of the document

This is a very common Russian pattern:

• копия документа — a copy of the document
• название книги — the title of the book
• страница журнала — the page of the magazine

So документа is not the subject here. The whole phrase оригинал документа is the subject, and документа depends on оригинал.

Literally, it is the original of the document.

In natural English, this often corresponds to:

• the original document
• the original copy of the document

Russian uses оригинал + genitive very naturally to mean the original version of something:

• оригинал письма — the original of the letter
• оригинал договора — the original of the contract

So even though the structure is literally original of document, the practical meaning is usually just the original document.

Готов is the short form of the adjective готовый.

In Russian, short-form adjectives are often used:

• as part of the predicate
• to express a temporary state or condition

So:

• Оригинал документа уже готов. — The original document is already ready.

Compare:

• готовый документ — a ready/prepared document
  Here готовый is the full form, used before a noun.
• Документ готов. — The document is ready.
  Here готов is the short form, used after the noun as the predicate.

This is a very common pattern:

• дом высокий — a tall house
• дом высок — the house is tall

Not every adjective uses short forms equally often in modern Russian, but готов is extremely common.

Yes. Готов agrees with the noun it describes, which is оригинал.

Оригинал is:

• masculine
• singular
• nominative

So the short-form adjective must also be masculine singular:

• готов — masculine singular
• готова — feminine singular
• готово — neuter singular
• готовы — plural

Examples:

• Копия готова. — The copy is ready.
  (копия is feminine)
• Письмо готово. — The letter is ready.
  (письмо is neuter)
• Документы готовы. — The documents are ready.
  (документы is plural)

So готов is used because оригинал is masculine singular.

Уже means already.

It shows that the state has been reached by this point:

• Оригинал документа готов. — The original document is ready.
• Оригинал документа уже готов. — The original document is already ready.

So уже adds the idea of earlier than expected, by now, or at this point.

Its position here is natural and neutral. Russian word order is flexible, but уже often stands close to the word or idea it modifies.

Yes, Russian word order is fairly flexible, although the neutral order here is very natural:

• Оригинал документа уже готов.

Other orders are possible, for example:

• Оригинал документа готов уже.
• Уже готов оригинал документа.

These can sound more marked, stylistic, or context-dependent.

A rough guide:

• Оригинал документа уже готов. — neutral, standard
• Уже готов оригинал документа. — emphasizes that it is now ready
• Оригинал документа готов уже. — possible, but often more conversational or contrastive depending on context

So yes, the order can change, but the given version is probably the best default one for a learner to use.

The stress is:

• оригина́л документа́ уже́ гото́в

Word by word:

• оригина́л
• документа́
• уже́
• гото́в

Stress is very important in Russian, because it is not always predictable. For learners, it helps to memorize stressed syllables together with the word.

Yes, absolutely — but it means something slightly different.

• Документ уже готов. — The document is already ready.
• Оригинал документа уже готов. — The original of the document is already ready.

The second sentence specifically refers to the original, not just the document in general. This can matter in real contexts where there may also be:

• a copy
• a draft
• a scan
• a translated version

So оригинал документа is more specific than simply документ.

Usually готов means ready, but in many contexts English might translate it as finished, done, or completed, depending on what sounds natural.

For example:

• Обед готов. — Dinner is ready.
• Доклад готов. — The report is ready / finished.
• Оригинал документа уже готов. — The original document is already ready / finished.

So the core idea is that something has been prepared and is now in a usable final state. The best English translation depends on context.