Носоупор уже установлен.

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

So where English says:

• The nose support is already installed

Russian simply says:

• Носоупор уже установлен

A form of быть would appear in the past or future, for example:

• Носоупор был установлен = The nose support was installed
• Носоупор будет установлен = The nose support will be installed

So the sentence sounds completely normal without any separate word for is.

Установлен is the short-form passive participle of установить.

That means it expresses a resulting state in a passive sense: something has been installed / is installed.

Compare:

• установить = to install, to set up
• установлен = installed (short form, used as the predicate)

This is very common in Russian, especially in technical, formal, and written language.

For example:

• Прибор установлен. = The device is installed.
• Программа уже установлена. = The program is already installed.

Because this sentence uses the short form, not the full form.

• установлен = short form, typically used after the noun as the main statement
• установленный = full form, usually used like an adjective before or with a noun

So:

• Носоупор уже установлен. = The nose support is already installed.
• установленный носоупор = an installed nose support

In other words:

• short form = “is installed”
• full form = “installed” as a describing word before a noun

The ending matches the gender and number of the noun it refers to.

Here, носоупор is masculine singular, so the short-form participle is:

• установлен = masculine singular

Other forms would be:

• установлена = feminine singular
• установлено = neuter singular
• установлены = plural

Examples:

• Линза уже установлена. = feminine
• Устройство уже установлено. = neuter
• Детали уже установлены. = plural

A Russian noun ending in a hard consonant is usually masculine, and носоупор ends in -р.

So it behaves like a masculine noun:

• носоупор
• новый носоупор
• носоупор установлен

Even if it is a compound technical word, it still follows normal gender rules based on its form.

Уже means already.

It tells you that the installation has been completed by now, often with the idea that this happened earlier than expected or that the state is now true.

So:

• Носоупор установлен. = The nose support is installed.
• Носоупор уже установлен. = The nose support is already installed.

The word уже often appears before the short-form predicate, just as it does here.

It mainly describes a state resulting from a completed action.

That is one of the key uses of short-form passive participles in Russian. The sentence does not focus on who installed it or when exactly. Instead, it presents the current situation:

• the item is now in the installed state

So a natural English understanding is often either:

• has already been installed or
• is already installed

Which one sounds better depends on context.

Yes, Russian word order is flexible.

The neutral order here is very natural:

• Носоупор уже установлен.

But you could also hear:

• Носоупор установлен уже.
• Уже установлен носоупор.

These versions shift the emphasis a bit:

• Носоупор уже установлен = neutral, straightforward
• Носоупор установлен уже = stronger focus on already
• Уже установлен носоупор = more formal or marked, often used for emphasis or in technical descriptions

For most learners, the original order is the safest and most standard.

Установить is perfective.

That matters because the sentence refers to a completed result: the item has been installed.

The imperfective partner is usually:

• устанавливать = to be installing / to install repeatedly or as a process

So:

• установить focuses on completion
• устанавливать focuses on process or repeated action

The participle установлен comes from the perfective verb and naturally suggests a completed installation.

Not exactly.

• Носоупор уже установлен. = The nose support is already installed / has already been installed
  This usually refers to the current state.

• Носоупор уже был установлен. = The nose support had already been installed / was already installed
  This places the statement in the past.

So adding был moves the sentence away from the present and into a past-time frame.

Yes, very natural.

This kind of structure is especially common in:

• manuals
• product descriptions
• assembly instructions
• technical specifications
• status messages

Russian often uses short-form passive participles in this style because they are concise and formal:

• Кронштейн установлен.
• Фильтр заменён.
• Сервер настроен.

So Носоупор уже установлен sounds exactly like the kind of sentence you might see in product documentation.