Тихая зона отделяется от общей зоны.

Because it is the grammatical subject of the sentence: the thing being described.

• тихая зона = the quiet zone
• отделяется = is separated / gets separated
• от общей зоны = from the common/general zone

Russian word order is more flexible than English word order, but here the sentence starts with what the speaker wants to talk about first: the quiet zone.

Because the preposition от requires the genitive case.

So:

• dictionary form: общая зона
• after от: от общей зоны

This is very common in Russian: a preposition changes the case of the noun phrase that follows it.

Here, от means from, so от общей зоны literally means from the common/general zone.

Because they are in different cases.

Both adjectives agree with зона, but each phrase has a different grammatical role:

• тихая зона = nominative case
• от общей зоны = genitive case

So the adjective changes too:

• тихая matches nominative feminine singular
• общей matches genitive feminine singular

The noun also changes:

• зона
• зоны

This is normal adjective-noun agreement in Russian.

Отделяется comes from отделяться, which means to be separated, to become separated, or sometimes to be set apart.

The -ся ending often gives a reflexive or passive-like meaning. In this sentence, it makes the verb sound like:

• is separated
• gets separated
• is set apart

So Тихая зона отделяется от общей зоны is not saying that the quiet zone is separating something else. It says that the quiet zone is separated from the general area.

Yes, it is present tense, 3rd person singular.

Formally, it means separates itself / is separating, but in many contexts Russian uses this kind of verb where English prefers a passive-style translation:

• отделяется → is separated
• sometimes also is being separated or gets separated

In signs, rules, or descriptions of layouts, the best natural English translation is usually is separated from.

Общий can mean several related things, including:

• common
• general
• shared

In общая зона, it usually means something like:

• the general area
• the shared area
• the main/common area

So depending on context, общая зона may sound more natural in English as general zone/area or common area rather than literally common zone.

Yes. Russian word order is flexible.

For example, you could also say:

• От общей зоны отделяется тихая зона.

This still means roughly the same thing, but the emphasis changes.

• Тихая зона отделяется от общей зоны focuses first on the quiet zone
• От общей зоны отделяется тихая зона starts with from the general area, which may sound more descriptive or contrastive

The original order is very natural, especially in a neutral statement.

Usually, no—not in a normal standalone sentence like this.

Russian can sometimes omit a noun if it is very obvious from context, but here от общей зоны is the full and natural phrase. Saying only от общей would sound incomplete in most situations.

So repeating зона is normal:

• тихая зона
• общая зона

English might avoid repetition more often, but Russian is perfectly comfortable with it.

The stress is:

• отделЯется

So the stressed syllable is я.

A rough pronunciation guide is:

• ти́хая → TEE-kha-ya
• зо́на → ZO-na
• отделя́ется → at-dee-LYA-yet-sa
• от → ot
• обще́й → ab-SHYEY
• зо́ны → ZO-ny

A learner should especially notice:

• -тся / -ется is pronounced -ца / -ецца in normal speech
• общей has the щ sound, which is softer and longer than English sh

Yes. That is also correct, but it is slightly different in form.

• отделяется = is separated / gets separated / is set apart
• отделена = is separated (short-form passive participle, more like a state/result)

Compare them:

• Тихая зона отделяется от общей зоны
  More verbal, describing how it is separated or presented as a general rule.

• Тихая зона отделена от общей зоны
  More focused on the resulting state: the quiet zone is separated from the common area.

In many contexts, both are possible. The original sentence with отделяется is especially natural in formal descriptions, instructions, or signage.