Documentul este necesar.

Because Romanian usually puts the definite article at the end of the noun, not before it.

• document = a document
• documentul = the document

So -ul is the masculine/neuter singular definite article attached to the noun.

This is one of the biggest differences from English:

• English: the document
• Romanian: documentul

Este means is. It is the 3rd person singular present form of a fi (to be).

So the structure is:

• Documentul = the document
• este = is
• necesar = necessary

Together: The document is necessary.

Not in this sentence if you want a full statement.

• Documentul este necesar. = The document is necessary.
• Documentul necesar = the necessary document

So without este, it stops being a complete sentence and becomes a noun phrase.

Because necesar is an adjective here, and it is used predicatively after este.

In Romanian, predicate adjectives normally do not take the definite article:

• Documentul este necesar. = The document is necessary.

But if the adjective is part of a noun phrase, the pattern changes:

• documentul necesar = the necessary document

So in your sentence, necesar is correct because it describes the subject through the verb este.

Yes. Document is a neuter noun in Romanian.

Neuter nouns in Romanian behave:

• like masculine in the singular
• like feminine in the plural

That is why you get:

• singular: documentul este necesar
• plural: documentele sunt necesare

Notice how the adjective changes:

• necesar for singular
• necesare for plural

It becomes:

Documentele sunt necesare. = The documents are necessary.

Changes:

• documentul → documentele
• este → sunt
• necesar → necesare

This shows agreement in number.

The normal, neutral order is:

Documentul este necesar.

This is the most natural way to say it in most contexts.

Romanian word order can sometimes change for emphasis, but for a learner, this standard order is the safest choice:

• subject
• verb
• adjective/complement

A rough pronunciation is:

do-ku-MEN-tool ES-te ne-che-SAR

A few helpful points:

• c before u in documentul sounds like k
• ce in necesar sounds like che in check
• stress usually falls like this:
  • docuMENtul
  • ESte
  • neceSAR

A more IPA-style version is: /dokuˈmentul ˈeste net͡ʃeˈsar/

No, not as written.

• Documentul este necesar. = The document is necessary.
• Documentul necesar. = The necessary / required document.

So the presence of este makes it a full statement, not just a noun phrase.

Yes, but it means something slightly different.

• Documentul este necesar. = The document is necessary.
• Un document este necesar. = A document is necessary.

So the difference is the same as in English:

• the document = a specific document
• a document = any one document / an unspecified document

Not exactly.

Necesar usually means:

• necessary
• needed
• required in a general sense

But mandatory / compulsory is often better translated by obligatoriu.

So:

• Documentul este necesar. = The document is necessary / needed.
• Documentul este obligatoriu. = The document is mandatory.

The difference is subtle but important.

Romanian often omits subject pronouns like eu, tu, el, because the verb already shows the person.

But here the subject is a full noun, documentul, and it carries the main meaning. If you remove it, you get:

• Este necesar. = It is necessary.

That is grammatical, but it no longer means exactly The document is necessary. It becomes more general.