Мне нравится запах свежего хлеба на кухне.

Because нравиться works differently from English to like.

In Russian, the idea is closer to something is pleasing to someone.

So in this sentence:

• мне = to me
• нравится = is pleasing / is liked
• запах свежего хлеба = the smell of fresh bread

So literally, the sentence is something like:

To me is pleasing the smell of fresh bread in the kitchen.

That is why the person who experiences the liking is in the dative case: мне.

Мне is the dative case form of я.

Here are the forms:

• я = I
• меня = me
• мне = to me

With нравиться, Russian uses the person in the dative:

• мне нравится = I like
• тебе нравится = you like
• ему нравится = he likes
• нам нравится = we like

So мне is used because the structure is to me, it is pleasing.

Because the grammatical subject is запах, and запах is singular.

Compare:

• Мне нравится запах. = I like the smell.
• Мне нравятся запахи. = I like the smells.

The verb agrees with the thing that is liked, not with мне.

In this sentence:

• запах = singular
• so → нравится

If the subject were plural, you would use нравятся.

Запах is in the nominative case.

Even though English learners often expect the thing after like to be an object, with нравиться the thing liked behaves like the subject of the sentence.

So:

• Мне нравится запах.
• literally: The smell is pleasing to me.

That is why запах is nominative.

Because запах often takes the genitive case to show the smell of something.

So:

• запах хлеба = the smell of bread
• запах кофе = the smell of coffee
• запах моря = the smell of the sea

That is why хлеб becomes хлеба.

And because adjectives must agree with the noun they describe, свежий also changes to genitive singular:

• свежий хлеб → nominative
• свежего хлеба → genitive

So запах свежего хлеба means the smell of fresh bread.

Because it agrees with хлеба, which is:

• masculine
• singular
• genitive

The adjective свежий has to match the noun:

• nominative masculine singular: свежий хлеб
• genitive masculine singular: свежего хлеба

So the ending changes because the case changes.

Because на кухне means in the kitchen when talking about location.

With на:

• на кухню = to the kitchen (direction, accusative)
• на кухне = in/on the kitchen, meaning in the kitchen (location, prepositional)

Russian often uses на with some rooms and places where English uses in.
So you simply learn the natural phrase:

• на кухне = in the kitchen

It most naturally describes where the smell is being experienced or where the smell is present:

I like the smell of fresh bread in the kitchen.

In context, it usually means the smell of fresh bread when it is in the kitchen.

But prepositional phrases in Russian can sometimes be a little flexible. Depending on context, it could feel like:

• the smell that is in the kitchen
• the smell of bread on/in the kitchen setting

If you wanted to stress that the smell is coming from the kitchen, Russian would often use:

• с кухни = from the kitchen

For example:

• Мне нравится запах свежего хлеба с кухни.
  = I like the smell of fresh bread coming from the kitchen.

Yes, you can, but it is slightly different in tone.

• Мне нравится запах... = I like the smell...
• Я люблю запах... = I love the smell... / I really like the smell...

In many contexts:

• нравится sounds more neutral and common for ordinary liking
• люблю sounds stronger, more emotional, or more personal

So both are correct, but мне нравится is often the more natural choice for a simple statement of liking.

Yes. Russian word order is flexible.

The neutral order here is:

• Мне нравится запах свежего хлеба на кухне.

But you could also say:

• Запах свежего хлеба на кухне мне нравится.
• На кухне мне нравится запах свежего хлеба.

The basic meaning stays similar, but the emphasis changes:

• starting with мне highlights to me
• starting with запах highlights the smell
• starting with на кухне highlights in the kitchen

So word order in Russian often helps show focus rather than changing the basic grammar.

Because Russian has no articles like a or the.

So:

• запах can mean a smell or the smell
• хлеб can mean bread, a bread, or sometimes the bread, depending on context

English has to choose:

• I like the smell of fresh bread in the kitchen
• I like a smell of fresh bread... — which sounds less natural in English

Russian does not make that distinction with articles. You understand it from context.

Not necessarily.

Запах is a neutral word meaning smell/odor. It can be pleasant or unpleasant depending on context.

Examples:

• приятный запах = a pleasant smell
• неприятный запах = an unpleasant smell

In this sentence, because it is about fresh bread, the smell is clearly pleasant.
So in English, smell works well, though aroma could also fit stylistically.

Because Russian usually omits to be in the present tense when it is just linking things, but here the main verb is not to be anyway.

The main verb is:

• нравится = is pleasing / is liked

So the sentence already has a full verb.

If you are expecting something like is, English and Russian just structure the idea differently here.

You would usually say:

• Мне не нравится запах свежего хлеба на кухне.

That means:

• I don’t like the smell of fresh bread in the kitchen.

The negative particle не goes before the verb:

• нравится → не нравится

That is the normal way to negate this sentence.

The simplest way is just to use intonation:

• Тебе нравится запах свежего хлеба на кухне?
  = Do you like the smell of fresh bread in the kitchen?

Russian often forms yes/no questions without changing word order.
You just raise your intonation, especially near the end or on the important word.

You could also change мне to another dative pronoun:

• тебе нравится...? = do you like...?
• вам нравится...? = do you like...? (formal/plural)