هذا الحي هادئ في الصباح، لكنه ليس هادئا في المساء.

In Arabic, a present-tense sentence like this neighborhood is quiet usually has no separate word for is. So هذا الحي هادئ is literally this neighborhood quiet, but it means this neighborhood is quiet.

That is very normal in Arabic.
When Arabic wants to negate this kind of sentence, it often uses ليس, which is why the second clause says ليس هادئًا.

Because هذا الحي means this neighborhood: the demonstrative هذا is directly modifying a definite noun.

In standard Arabic, when هذا / هذه means this before a specific noun, that noun is usually also definite with الـ:

• هذا الحي = this neighborhood
• هذا البيت = this house

Without الـ, the structure usually changes:

• هذا حيٌّ would normally be understood more like this is a neighborhood

So هذا الحي is the normal form here.

Because الحيّ is a masculine singular noun.

Arabic demonstratives must agree with the noun in gender and number:

• هذا = masculine singular
• هذه = feminine singular

So:

• هذا الحي = correct
• هذه الحي = not correct

It is pronounced al-ḥayy.

A few useful points:

• The first consonant is ح, a stronger, breathier sound than English h
• The final ي is effectively doubled here, so you hear -yy
• In fully inflected formal reading, you may hear al-ḥayyu

So a learner-friendly pronunciation is al-ḥayy.

Because here it is a predicate adjective, not an adjective directly attached to the noun.

Compare:

• الحي هادئ = the neighborhood is quiet
• الحي الهادئ = the quiet neighborhood

So in your sentence, هادئ is describing the subject as the predicate of the sentence, and that is why it appears without الـ.

This is a case-ending question.

In full formal grammar:

• هادئٌ is nominative in هذا الحي هادئٌ
• هادئًا is accusative after ليس in ليس هادئًا

So the difference comes from grammar, not from a change in meaning.

A simplified way to think about it:

• plain nominal sentence → predicate is usually nominative
• after ليس → predicate becomes accusative

In normal unvocalized Arabic, the first word is often just written هادئ without showing the final short vowel. The second one is often written in a way that makes the accusative more visible: هادئًا.

Because ليس is the normal MSA way to negate a sentence with a noun or adjective in the present/general sense.

So:

• الحي هادئ = the neighborhood is quiet
• الحي ليس هادئًا = the neighborhood is not quiet

Using لا here would not be the normal standard pattern for this kind of sentence.

لكنه means but it or however, it and refers back to الحي.

In fully vocalized writing, it is لكنَّهُ. In ordinary Arabic writing, the short vowels and shadda are usually not written, so you often just see لكنه.

It is a smooth way to avoid repeating the noun:

• هذا الحي هادئ في الصباح، لكنه ليس هادئًا في المساء = This neighborhood is quiet in the morning, but it is not quiet in the evening

You could repeat the noun, but this version sounds more natural and less repetitive.

Because ص is a sun letter.

With sun letters, the l of الـ is not pronounced; it assimilates to the next sound. So:

• الصباح is pronounced aṣ-ṣabāḥ

But المساء begins with م, which is a moon letter, so the l is pronounced:

• المساء = al-masāʾ

And الحي also keeps the l sound because ح is a moon letter:

• الحي = al-ḥayy

After the preposition في, the noun is in the genitive case.

So in fully vocalized Arabic, you would read:

• في الصباحِ
• في المساءِ

Most Arabic texts do not write the short vowels, so you usually just see:

• في الصباح
• في المساء

But grammatically, both nouns are genitive because of في.

Yes. That is also good Arabic.

You can use a time expression directly in the accusative:

• هذا الحي هادئ صباحًا، لكنه ليس هادئًا مساءً

That also means This neighborhood is quiet in the morning, but not in the evening.

So both patterns are possible:

• في الصباح / في المساء
• صباحًا / مساءً

The version with في is especially clear and straightforward for learners.