Для продления нужна госпошлина.

Because для normally requires the genitive case.

• Dictionary form: продление = renewal, extension
• Genitive singular: продления

So для продления literally means for renewal or for the renewal/extension.

This is a very common pattern in Russian:

• для работы = for work
• для учебы = for studying / for study
• для оформления = for processing / for оформление-related paperwork

No. It is a noun, not a verb.

The base noun is продление, which comes from the verb продлить = to extend / renew. English often uses either a noun or a verb in this kind of phrase, but Russian often prefers a noun after для.

So:

• продлить = to renew, to extend
• продление = renewal, extension
• для продления = for renewal

Because для is followed by a noun phrase, not an infinitive.

So Russian says:

• для продления = for renewal

not:

• для продлить ✘

If you want a verb-based structure, Russian would normally use something like:

• чтобы продлить = in order to renew
• нужно продлить = it is necessary to renew

So для продления is the natural bureaucratic-style way to say for renewal.

Because нужна agrees with госпошлина, and госпошлина is feminine singular.

Forms of нужен:

• нужен = masculine singular
• нужна = feminine singular
• нужно = neuter singular
• нужны = plural

Examples:

• Нужен паспорт. = A passport is needed.
• Нужна госпошлина. = A state fee is needed.
• Нужно разрешение. = A permit is needed.
• Нужны документы. = Documents are needed.

Grammatically, госпошлина is the thing that is needed, so it is in the nominative case, not the accusative.

That can feel unusual to an English speaker, because English says you need a fee, where a fee looks like an object. But Russian often uses a different structure:

• нужен / нужна / нужно / нужны
  • nominative noun

So in this sentence:

• госпошлина is nominative singular
• нужна agrees with it

Literally, the structure is closer to A state fee is necessary.

Госпошлина is short for государственная пошлина.

It means a state fee, government fee, or official duty/charge paid to a government authority for some administrative service.

It is a common word in official and bureaucratic Russian, especially for things like:

• passports
• visas
• court filings
• registrations
• renewals

So in this sentence it means the official government fee required for the renewal.

Because in the present tense, Russian usually does not use a separate verb for to be.

So:

• Для продления нужна госпошлина.

literally looks like:

• For renewal needed state fee.

But in natural English it means:

• A state fee is needed for renewal.

This is completely normal Russian grammar.

Yes. Russian word order is flexible, and the sentence can be rearranged depending on emphasis.

For example:

• Для продления нужна госпошлина.
• Госпошлина нужна для продления.

Both are correct.

The version with Для продления first puts the focus on the context/purpose: as for renewal...

The version with Госпошлина first puts the focus more on the fee itself.

In official notices, putting the purpose first is very common.

Yes, it sounds fairly official or administrative.

Russian bureaucracy often uses compact noun-based expressions like:

• для продления
• для оформления
• для получения
• требуется
• необходима
• нужна

So this sentence sounds like something you might read on a website, on a form, or in an office notice.

Yes. Those are close in meaning, but the tone changes slightly.

• нужна госпошлина = a state fee is needed
• требуется госпошлина = a state fee is required
• необходима госпошлина = a state fee is necessary

All are possible, but:

• нужна is straightforward and common
• требуется sounds more official
• необходима sounds formal/bookish

So the original sentence is natural and clear, especially in practical official contexts.