Строительные леса уже установлены.

Yes, лес usually means forest. But строительные леса is the normal Russian term for scaffolding.

A few important points:

• In this meaning, Russian uses a plural form: леса.
• English often treats scaffolding as singular, but Russian treats леса as plural.
• Historically, the word is connected with wooden framework, which is why it looks like the plural of лес.

So Строительные леса means construction scaffolding, not construction forests in any literal modern sense.

Here строительные леса is in the nominative plural, because it is the subject of the sentence.

The adjective строительные agrees with леса in:

• number: plural
• gender: not relevant in the plural
• case: nominative

That is why you get:

• строительные леса = nominative plural

If the case changed, the adjective would change too.

Установлены is a short passive participle from установить.

In practice, it works as the main predicate of the sentence and means something like:

• have been installed
• are installed
• have already been set up

This is very common in Russian.

Compare:

• установленные леса = installed scaffolding
  
  • full form, used like an adjective before the noun
• леса установлены = the scaffolding is installed / has been installed
  
  • short form, used as the predicate

So in this sentence, установлены is not just describing the noun; it is telling you the state/result.

Because леса is plural, and the short passive participle has to agree with it.

Compare:

• мост установлен = the bridge is installed
• дверь установлена = the door is installed
• окно установлено = the window is installed
• леса установлены = the scaffolding is installed

So the ending changes to match the subject.

Russian usually does not use a present-tense copula in neutral statements.

So where English says:

• The scaffolding is installed

Russian simply says:

• Леса установлены

There is no separate present-tense to be here.

In other tenses, you do get a form of быть:

• Строительные леса были установлены = The scaffolding was installed
• Строительные леса будут установлены = The scaffolding will be installed

It describes a completed result.

Установлены comes from установить, which is a perfective verb. That gives the idea that the action has been completed and the result now exists.

So the sentence means something like:

• The scaffolding has already been installed
• The scaffolding is already set up

It does not mean the scaffolding is being installed right now.

For an ongoing process, Russian would use a different form, for example:

• Строительные леса устанавливают = They are installing the scaffolding
• Строительные леса устанавливаются = The scaffolding is being installed

Уже means already.

In this sentence, it shows that the installation is complete earlier than expected or by this point in time:

• Строительные леса уже установлены = The scaffolding has already been installed

Its position is fairly natural here: after the subject and before the predicate.

Russian word order is flexible, so you can move уже for emphasis, for example:

• Уже установлены строительные леса
• Строительные леса установлены уже

But Строительные леса уже установлены is the most neutral and natural version.

Yes, absolutely, if the context is clear.

In a construction context, леса by itself is often enough to mean scaffolding:

• Леса уже установлены

Adding строительные makes it more explicit and slightly more formal or descriptive:

• Строительные леса уже установлены

So both are possible; the longer version is just clearer out of context.

Because Russian, like English, often uses this kind of construction when the result is more important than the person who did the action.

This sentence focuses on the state of the scaffolding:

• Строительные леса уже установлены = the important fact is that the scaffolding is now in place

If you want to name the doer, you would use an active sentence instead:

• Рабочие уже установили строительные леса = The workers have already installed the scaffolding

So the passive-like form is chosen because the agent is unimportant or obvious.

Yes, that is a very good idea.

Even though each word is understandable on its own, строительные леса is a standard set phrase meaning scaffolding. Learners usually understand it more easily if they memorize it as one unit.

Useful related forms:

• строительные леса = scaffolding
• на строительных лесах = on the scaffolding
• монтаж строительных лесов = installation of scaffolding
• демонтаж строительных лесов = dismantling of scaffolding

So yes: treat строительные леса as a common construction term, not as a word-for-word literal phrase.