Ответ нужен немедленно.

Нужен is the short-form adjective of нужный, and in this sentence it means needed or necessary.

So Ответ нужен немедленно is literally something like:

• The answer is needed immediately
• or more naturally, An answer is needed immediately

In Russian, short-form adjectives are very common in this kind of statement:

• нужен — needed/necessary for a masculine singular noun
• нужна — for a feminine singular noun
• нужно — for a neuter singular noun
• нужны — for plural nouns

Because ответ is a masculine singular noun, and нужен agrees with it.

Agreement here works like this:

• ответ нужен — answer is masculine singular
• книга нужна — book is feminine singular
• письмо нужно — letter is neuter singular
• документы нужны — documents is plural

So the form of нужен is chosen to match ответ.

Because ответ is the thing that is needed, and in this structure Russian treats that noun as the main noun of the sentence.

So:

• Ответ нужен. = An answer is needed.

The noun being needed is normally in the nominative.

Compare:

• Мне нужен ответ. — I need an answer.
  • мне = to me / I
  • ответ = nominative, the thing needed

This is different from English, where we usually make the person the subject: I need an answer.
Russian often uses a structure closer to To me, an answer is needed.

It is simply not stated in this sentence.

Russian often leaves that part out when it is obvious from context.
A fuller version could be:

• Мне нужен ответ немедленно. — I need an answer immediately.
• Нам нужен ответ немедленно. — We need an answer immediately.

So Ответ нужен немедленно focuses on the urgent need for the answer itself, without saying exactly who needs it.

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

So where English says:

• The answer is needed immediately

Russian simply says:

• Ответ нужен немедленно

This is completely normal. Russian does not normally insert a present-tense is here.

Немедленно is an adverb meaning immediately, without delay, or at once.

It tells you how urgently the answer is needed.

So:

• Ответ нужен немедленно.
• literally: The answer is needed immediately.

It is not describing the noun ответ. It is modifying the whole situation: the need is immediate.

Because the sentence needs an adverb, not an adjective.

• немедленный = immediate — an adjective, used with nouns
• немедленно = immediately — an adverb, used with actions or situations

Examples:

• немедленный ответ — an immediate answer
• Ответ нужен немедленно — An answer is needed immediately

So in your sentence, the adverb is the correct choice.

Yes. Russian word order is more flexible than English, and changing it usually changes the focus or emphasis, not the basic meaning.

For example:

• Ответ нужен немедленно. — neutral; an answer is needed immediately
• Немедленно нужен ответ. — stronger emphasis on immediately
• Нужен ответ немедленно. — also possible, with emphasis shifted toward needed

The original sentence sounds natural and straightforward.

It can mean either, depending on context.

Russian has no articles like a or the, so ответ by itself does not tell you whether it is definite or indefinite.

Depending on the situation, it could be understood as:

• the answer
• an answer

That is normal in Russian, and context tells you which meaning is intended.

It sounds direct and urgent, but not unusually formal.

It could fit in:

• business communication
• official requests
• urgent conversations
• written messages

Because it omits the person who needs the answer, it can sound a little more impersonal or businesslike than:

• Мне нужен ответ немедленно.
• Нам нужен ответ немедленно.

But it is still very natural Russian.