Согласно правилу, гостевой пропуск нужен у входа.

Because согласно requires the dative case.

• Dictionary form: правило = rule
• Dative singular: правилу

So согласно правилу means according to the rule.

This is something you usually just memorize with the word согласно:

• согласно плану = according to the plan
• согласно закону = according to the law
• согласно правилу = according to the rule

Here согласно is a preposition meaning according to.

In modern Russian, when it is used this way, it is followed by the dative case:

• согласно приказу
• согласно расписанию
• согласно правилу

So in this sentence, treat согласно as a fixed preposition + dative pattern.

Because согласно правилу is an introductory adverbial phrase placed at the beginning of the sentence.

Russian often separates this kind of opening phrase with a comma, especially when it sets the context:

• Согласно правилу, ...
• По словам учителя, ...
• По плану, ...

The comma helps mark the phrase as background information before the main statement.

Because нужен agrees with гостевой пропуск, which is masculine singular.

Forms of нужен change like a short-form adjective:

• masculine: нужен
• feminine: нужна
• neuter: нужно
• plural: нужны

Since пропуск is masculine singular, Russian says:

• пропуск нужен

Compare:

• Книга нужна.
• Письмо нужно.
• Документы нужны.

Because in the present tense, Russian usually leaves out the verb to be.

So instead of saying something like The guest pass is needed, Russian simply says:

• гостевой пропуск нужен

This is completely normal. In past or future tense, a form of быть would appear:

• Гостевой пропуск был нужен. = The guest pass was needed.
• Гостевой пропуск будет нужен. = The guest pass will be needed.

Yes. Гостевой пропуск is in the nominative case and functions as the subject-like element: the thing that is needed.

A useful pattern is:

[thing in nominative] + нужен / нужна / нужно / нужны + [place/person/context]

For example:

• Паспорт нужен здесь.
• Билет нужен при входе.
• Гостевой пропуск нужен у входа.

So the sentence is built around the guest pass is needed.

Гостевой means guest or visitor-related.

It comes from гость = guest. In combinations like this, it describes something intended for visitors:

• гостевой пропуск = guest pass / visitor pass
• гостевая виза = guest visa
• гостевой дом = guest house

So гостевой пропуск is not just any pass; it is specifically a pass for a guest or visitor.

Here пропуск means pass, permit, or access pass.

This is a useful word because it can have more than one meaning in Russian depending on context. For example, it can also mean:

• a skipped class
• an omission
• a gap

But in security or building-entry contexts, пропуск very often means:

• entry pass
• access card
• permit

So in this sentence, гостевой пропуск clearly means visitor pass.

У входа means by the entrance, near the entrance, or at the entrance.

The preposition у requires the genitive case, so:

• dictionary form: вход
• genitive singular: входа

So:

• у входа = at/by the entrance

This is a common pattern:

• у двери = by the door
• у окна = by the window
• у дома = by the house

Here it gives the location where the pass is needed.

Yes, and the meaning would be similar, but the nuance is slightly different.

• у входа = at/by the entrance, focusing on location
• при входе = upon entering / at the entrance, often focusing more on the moment or circumstance of entry

So:

• Гостевой пропуск нужен у входа = a guest pass is needed at the entrance
• Гостевой пропуск нужен при входе = a guest pass is needed when entering / at entry

Both are natural, but у входа sounds a bit more physical and location-based.

Yes, Russian word order is flexible.

The sentence:

• Согласно правилу, гостевой пропуск нужен у входа.

is a neutral, clear way to say it. But other word orders are possible depending on emphasis:

• У входа нужен гостевой пропуск.
  Emphasizes the location first.
• Гостевой пропуск у входа нужен.
  Can sound more contrastive or emphatic.
• Согласно правилу, у входа нужен гостевой пропуск.
  Also very natural.

Russian word order often changes to highlight what is new, important, or contrasted.

These words are related, but they are not the same.

• нужен = needed / required
• должен = must / is supposed to / is obliged to
• необходим = necessary, often more formal

So:

• Гостевой пропуск нужен у входа.
  A guest pass is needed at the entrance.
• Вы должны показать гостевой пропуск у входа.
  You must show the guest pass at the entrance.
• Гостевой пропуск необходим у входа.
  A guest pass is necessary at the entrance.
  This sounds more formal or official.

In your sentence, нужен is the most natural everyday choice.

No. Russian has no articles.

So гостевой пропуск can mean:

• a guest pass
• the guest pass

Which one is meant depends on context. Russian speakers understand this from the situation, not from an article.

That is why a short Russian sentence can correspond to more than one natural English version.