Диспетчерская уже открыта.

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

So:

• Диспетчерская уже открыта. = The dispatch office is already open.

If you were talking about the past or future, Russian would use forms of быть:

• Диспетчерская была открыта. = The dispatch office was open.
• Диспетчерская будет открыта. = The dispatch office will be open.

This missing-present-is is completely normal in Russian.

Диспетчерская usually means a dispatch office, control room, or dispatcher’s office, depending on context.

It is a very common type of Russian noun formed from an adjective and used as a noun. Historically, it comes from something like диспетчерская комната or диспетчерская служба, but in real usage the shortened form диспетчерская stands on its own.

So even though it looks adjective-like, here it functions as a noun.

That is because it comes from an adjective form that has become substantivized, meaning an adjective used as a noun.

Russian does this quite often:

• столовая = dining room / cafeteria
• приёмная = reception room / office
• ванная = bathroom
• диспетчерская = dispatch office / control room

These words still decline like feminine adjectives, but in the sentence they behave like nouns.

Открыта is the short form, while открытая is the full form.

In this sentence, Russian uses the short form because it is saying the current state of the place:

• Диспетчерская уже открыта. = The office is already open.

Compare:

• открытая дверь = an open door
  
  • full form, used before a noun as a description
• дверь открыта = the door is open
  
  • short form, used as the predicate

So here открыта matches диспетчерская in feminine singular, and it works like open in English.

For a learner, the most useful way to understand it here is: it acts like a predicate word meaning open.

Historically/grammatically, открыт / открыта / открыто / открыты is often treated as a short passive participle of открыть (to open), but in many everyday sentences it feels very adjective-like:

• Магазин открыт. = The store is open.
• Дверь открыта. = The door is open.

So in this sentence, you can safely read открыта as open, while remembering that Russian uses this short-form pattern very often.

Уже means already.

So the sentence means that the dispatch office is open already / now open.

In this sentence, уже comes before открыта, which is very natural:

• Диспетчерская уже открыта.

Russian word order is flexible, but moving уже can slightly change emphasis:

• Уже диспетчерская открыта. — marked, unusual in neutral speech
• Диспетчерская открыта уже. — possible, but emphasizes already more strongly

For normal neutral speech, Диспетчерская уже открыта is the best pattern.

In this sentence, it most naturally means open.

Even though the form comes from the verb открыть (to open), Russian often uses it to describe a resulting state:

• Дверь открыта. = The door is open.
• Магазин открыт. = The store is open.

So the idea is not mainly someone opened it, but rather it is now in the open state.

Because it agrees with диспетчерская, which is feminine singular.

Short forms change according to gender and number:

• masculine: открыт
• feminine: открыта
• neuter: открыто
• plural: открыты

So:

• магазин открыт = the store is open
• дверь открыта = the door is open
• окно открыто = the window is open
• двери открыты = the doors are open

Since диспетчерская is feminine singular, the correct form is открыта.

Yes, Russian word order is flexible, but different orders change the focus or emphasis.

Neutral order:

• Диспетчерская уже открыта.

Other possible orders:

• Уже открыта диспетчерская.
  This can sound more literary or can emphasize the fact that it is now open.

• Диспетчерская открыта уже.
  This puts stronger emphasis on already.

For a learner, the given order is the most standard and natural in ordinary conversation.

A natural pronunciation is:

• диспетчЕрская уже́ открытА

Stress:

• диспетче́рская
• уже́
• открыта́

A rough English-style approximation would be:

• dees-pye-CHER-ska-ya oo-ZHE ok-ry-TA

But it is better to listen to native audio, because unstressed vowels are reduced in real Russian speech.