Переговорная была занята, в то время как опенспейс был свободен.

Переговорная is a very common office word meaning meeting room or conference room.

Grammatically, it comes from the fuller phrase переговорная комната (meeting room), but in real usage комната is often dropped because it is obvious from context. So:

• переговорная комната = full form
• переговорная = normal shortened form

This kind of shortening is common in Russian.

It is feminine because the implied full noun is комната, which is feminine.

Even when Russian speakers shorten переговорная комната to just переговорная, the word still behaves like a feminine noun. That is why you get feminine agreement:

• переговорная была занята

Both была and занята are feminine singular.

Russian usually omits to be only in the present tense:

• Переговорная занята. = The meeting room is occupied.
• Опенспейс свободен. = The open space is free.

But in the past tense, Russian does use forms of быть:

• был = was, masculine
• была = was, feminine
• было = was, neuter
• были = were

So in your sentence:

• Переговорная была занята
• опенспейс был свободен

that is completely normal past-tense grammar.

Because Russian past-tense forms and adjectives agree with the grammatical gender of the noun.

• переговорная is feminine
  → была занята
• опенспейс is masculine
  → был свободен

So there are two kinds of agreement happening here:

1. the past-tense form of быть agrees with the noun
2. the adjective also agrees with the noun

That is why the forms are different.

These are short-form adjectives, which are very common in Russian when describing a state in the predicate.

Compare:

• занятая переговорная = an occupied meeting room
  
  • this is a full adjective before a noun
• переговорная занята = the meeting room is occupied
  
  • this is a short adjective used as part of the predicate

Likewise:

• свободный опенспейс = a free/open open-space area
• опенспейс свободен = the open space is free

So in your sentence, занята and свободен are the normal forms because the sentence is describing a condition or state.

Literally, в то время как means something like at the time when, but in many sentences it works more like while or whereas.

In this sentence, it mainly expresses contrast, not just simultaneity. So the sense is:

• the meeting room was occupied,
• whereas / while the open space was free.

So here it is closer to whereas than to a purely time-based while.

Because в то время как introduces a subordinate clause, and Russian normally separates that clause with a comma.

So:

• Переговорная была занята, в то время как опенспейс был свободен.

That comma is standard Russian punctuation.

Russian often uses commas in places where English might be a little looser or more style-dependent.

Yes. Опенспейс is a modern loanword used in office/business Russian. It means an open-plan office space.

It is treated as a masculine noun, mainly because it ends in a consonant, which is a very common masculine pattern in Russian.

In your sentence it is in the nominative singular:

• опенспейс был свободен

So even though it comes from English, it behaves like an ordinary Russian masculine noun in grammar.

Yes. In context, занята can mean several closely related things:

• physically occupied
• in use
• unavailable
• booked/reserved

With a meeting room, Russian speakers often use занята for any situation where you cannot use it right now, whether someone is inside it or it has already been reserved.

So the exact English wording depends on context, even though the Russian is the same.

Yes. A simpler and more conversational version would often use а:

• Переговорная была занята, а опенспейс был свободен.

This sounds more natural in everyday speech.

The difference is roughly:

• а = simple contrast, very common and neutral
• в то время как = more formal, more explicit contrast, sometimes a bit more written/bookish

So your original sentence is correct, but it may sound slightly more formal than everyday office speech.