В гостиной висит старая люстра.

Because в can require different cases depending on the meaning.

Here it means in / inside a place, with no movement, so Russian uses the prepositional case:

• гостиная → nominative
• в гостиной → prepositional, meaning in the living room

A useful contrast:

• в гостиной = in the living room (location)
• в гостиную = into the living room (motion toward)

So the ending changes because the noun is showing location.

Historically, it is an adjective used like a noun, and in modern Russian learners usually just treat it as a noun meaning living room.

That is why its case endings look adjective-like:

• nominative: гостиная
• prepositional: в гостиной
• accusative: в гостиную

So even though it means a room, its forms follow the pattern of a feminine adjective.

Russian usually does not use a present-tense verb meaning is/are in simple sentences like this.

But here Russian does even more than that: it uses a position/state verb.
Висит means is hanging.

So the sentence is not just saying that the chandelier exists in the living room. It is saying how it is located there: it is hanging.

Russian often uses verbs like:

• стоять = to stand
• лежать = to lie
• висеть = to hang

This is more natural in Russian than a plain there is structure.

Висит is the 3rd person singular present tense form of висеть.

So:

• infinitive: висеть = to hang
• висит = it hangs / is hanging

It is singular because the subject люстра is singular.

If the subject were plural, you would get:

• В гостиной висят старые люстры. = The old chandeliers are hanging in the living room.

Because люстра is the subject of the sentence, and subjects are normally in the nominative case.

Russian word order is much freer than English word order.
Even though люстра comes after висит, it is still the thing doing the hanging, so it stays nominative.

This sentence structure is very common in Russian:

• В гостиной висит старая люстра.

It starts with the location, then gives the verb, then introduces the thing located there.

In a more English-like order, you could also say:

• Старая люстра висит в гостиной.

Both are grammatical.

Because adjectives must agree with the noun they describe in gender, number, and case.

Here люстра is:

• feminine
• singular
• nominative

So the adjective must also be:

• feminine
• singular
• nominative

That gives:

• старая люстра

Compare:

• старый стол = an old table
• старая люстра = an old chandelier
• старое окно = an old window
• старые книги = old books

Yes. Russian word order is flexible, and changing it usually changes focus or emphasis, not the basic meaning.

For example:

• В гостиной висит старая люстра.
  Focuses naturally on the setting first: In the living room, there is an old chandelier hanging.

• Старая люстра висит в гостиной.
  Starts with the chandelier itself.

• Висит старая люстра в гостиной.
  Possible, but less neutral and more stylistically marked.

The original sentence sounds very natural if you are introducing what is in the room.

This is an important distinction.

• висеть = to be hanging
  This describes a state or position.

• вешать = to hang / to put up (imperfective)
  This describes the action of hanging something up.

• повесить = to hang / put up (perfective)
  Also the action, but as a completed event.

So:

• Люстра висит. = The chandelier is hanging.
• Он вешает люстру. = He is hanging the chandelier up.
• Он повесил люстру. = He hung the chandelier up.

In your sentence, the chandelier is already in that state, so висит is the right verb.

Because Russian has no articles.

English distinguishes:

• a chandelier
• the chandelier

Russian does not mark that directly with a separate word.
The listener understands from context whether the meaning is more like a or the.

So старая люстра can mean:

• an old chandelier
• the old chandelier

depending on the situation.

The main stresses are:

• в гостИной висИт стАрая лЮстра

Word by word:

• в
• гостИной
• висИт
• стАрая
• лЮстра

A rough English-style approximation would be:

• v gas-TEE-nay vee-SEET STAR-a-ya LYOO-stra

A couple of notes:

• The в is pronounced like v.
• The ending -ой in гостиной sounds roughly like -oy, but in connected speech it is often less strong than in English.
• Russian stress is important because it can change from form to form, so it is worth learning each stressed word as a whole.

It can correspond to both in English, but the Russian sentence is a bit more specific because of висит.

English often prefers there is when introducing something:

• There is an old chandelier in the living room.

Russian often prefers a location + position verb pattern:

• В гостиной висит старая люстра.

So the Russian sentence naturally combines both ideas:

• the chandelier is there
• and it is hanging

That is why a very literal translation may sound slightly more vivid than the usual English one.