Общая кухня и кофейная зона находятся наверху.

Because the subject has two things: общая кухня and кофейная зона.
When two nouns are joined by и and act together as the subject, Russian normally uses a plural verb.

• кухня находится = the kitchen is located
• зона находится = the zone is located
• кухня и зона находятся = the kitchen and the zone are located

They are in the nominative case because they are the subject of the sentence.

You can see that both noun phrases are in their dictionary form:

• кухня = nominative singular
• зона = nominative singular
• общая and кофейная match those nouns in gender, number, and case

Even though the whole subject is plural in meaning, each noun itself stays singular.

Because they are adjectives describing feminine singular nominative nouns.

• кухня is feminine, so: общая кухня
• зона is feminine, so: кофейная зона

That -ая ending is a very common adjective ending for feminine nominative singular.

Compare:

• masculine: общий
• feminine: общая
• neuter: общее
• plural: общие

Not usually. In this context, общая means shared, common, or communal.

So общая кухня is a kitchen used by everyone, such as in an office, dormitory, hostel, or shared building.

A native English speaker might expect general kitchen from the adjective, but that is usually not the natural meaning here.

Yes. Кофейная comes from кофе and means coffee-related.

So кофейная зона is something like:

• a coffee area
• a coffee station
• a coffee corner

It does not necessarily mean a café. It usually means a place where coffee is available or where people can make or drink coffee.

Находятся literally means something like are located.

It is a very normal way to talk about location, especially in neutral or slightly formal Russian. It sounds a bit more explicit than just giving the location.

Compare:

• Общая кухня и кофейная зона находятся наверху. = The shared kitchen and coffee area are located upstairs.
• Общая кухня и кофейная зона наверху. = The shared kitchen and coffee area are upstairs.

The second version is also possible in informal speech, but находятся is clear and standard.

Наверху is an adverb meaning:

• upstairs
• up above
• on the upper level

It is written as one word because it functions as a fixed adverb.

In this sentence, it means that the kitchen and coffee area are on a higher floor or higher level.

A useful thing to remember:

• наверху = upstairs / at the top
• внизу = downstairs / below

Yes. Russian word order is more flexible than English word order.

The original sentence is neutral and straightforward:

• Общая кухня и кофейная зона находятся наверху.

But you could also say:

• Наверху находятся общая кухня и кофейная зона.

That version puts more focus on наверху first, as if answering the question Where are they?

Both are grammatical. The difference is mainly emphasis and information flow, not basic meaning.

Because и is simply connecting two items in a single subject:

• общая кухня
• кофейная зона

In Russian, just like in English, you normally do not put a comma before и when it joins two words or phrases in a simple list or compound subject.

So this is correct:

• Общая кухня и кофейная зона находятся наверху.

If there were a more complex structure, comma rules could be different, but not here.