Мой брат уже женат.

Because брат is a masculine singular noun.

The possessive мой must agree with the noun it describes:

• мой брат = my brother
• моя сестра = my sister
• моё письмо = my letter
• мои друзья = my friends

So here мой is the correct masculine singular nominative form.

It is in the nominative case.

In this sentence, брат is the subject:

• Мой брат = my brother

Since the sentence is simply saying something about your brother, the subject stays in the nominative:

• брат = brother
• мой брат = my brother

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

So:

• Мой брат уже женат. literally looks like:
• My brother already married.

But in natural English, we translate it as:

• My brother is already married.

This is very normal in Russian:

• Он дома. = He is at home.
• Она счастлива. = She is happy.

Because женат is the normal Russian predicate used to say that a man is married.

It behaves like a short-form adjective/predicative word, not like an ordinary verb meaning to marry.

So:

• Он женат. = He is married.

Russian often expresses states this way rather than with a verb like English does.

If you want the action to marry / get married, you use other verbs, for example:

• жениться = to get married (for a man)
• выйти замуж = to get married (for a woman)

But in your sentence, we are talking about a state, not the action:

• already married, not already got married

Yes. Женат is used for a married man.

For a married woman, Russian normally uses:

• замужем

Examples:

• Мой брат женат. = My brother is married.
• Моя сестра замужем. = My sister is married.

This is an important difference from English, where married works for both men and women.

Уже means already.

So:

• Мой брат уже женат. = My brother is already married.

Depending on context, уже can also carry a nuance like:

• by now
• as early as now
• sometimes even mild surprise: already?

For example, it could suggest:

• he got married earlier than expected
• by this point, he is married

Yes, Russian word order is fairly flexible.

The neutral order here is:

• Мой брат уже женат.

But you may also hear:

• Мой брат женат уже.
• Уже мой брат женат. — possible, but more marked or context-dependent
• Женат мой брат уже. — strongly stylistic or emphatic

Even though word order can change, the most natural basic version for learners is:

• Мой брат уже женат.

Russian often changes word order for emphasis, contrast, or style, not because the grammar changes.

This is a very common question.

• женат = the normal predicate form meaning is married
• женатый = the full adjective form, usually used before a noun or in more descriptive contexts

Compare:

• Он женат. = He is married.
• женатый мужчина = a married man

In your sentence, Russian normally uses женат, not женатый:

• Мой брат уже женат. ✅
• Мой брат уже женатый. ❌ unnatural in standard usage for this meaning

So when you are simply saying someone is married, use женат.

In this sentence, уже modifies the whole idea that your brother is in the state of being married.

So the meaning is:

• My brother is already married not
• My already brother... which makes no sense in English or Russian

In practice, уже usually attaches to the predicate or the whole statement:

• Он уже дома. = He is already home.
• Она уже готова. = She is already ready.

So here it naturally means that the state married is already true.

It is pronounced approximately oo-ZHEH.

A few helpful points:

• the stress is on the second syllable: уже́
• the ж sounds like the s in measure
• the final е is pronounced like eh

So:

• уже́ ≈ oo-ZHEH

It is pronounced approximately zhy-NAT.

Helpful details:

• stress is on the second syllable: жена́т
• ж sounds like the s in measure
• the е in the first syllable is reduced because it is unstressed
• the final т is pronounced clearly

So:

• жена́т ≈ zhy-NAT

No. That would sound unnatural in standard modern Russian.

In present-tense sentences like this, Russian normally does not use есть to mean is.

So the correct sentence is:

• Мой брат уже женат.

The word есть exists in Russian, but it is not used the same way as English is in ordinary present-tense statements.

Yes, it sounds completely natural.

• Мой брат уже женат. is a normal everyday sentence.

It is simple, clear, and idiomatic. A native speaker would understand it immediately as a standard way to say that your brother is already married.