في المطبخ ثلاجة كبيرة، وفيها ماء وفاكهة.

Because Arabic often introduces existence by starting with the place first.

So في المطبخ ثلاجة كبيرة is a very natural way to say:

In the kitchen, there is a big refrigerator.

This is a common Arabic pattern:

• في البيت طفل
• On/In the house, there is a child → There is a child in the house

Arabic often puts the location first when it wants to present something as existing in that place.

In present-tense Arabic, you often do not need a verb for is / are / there is / there are.

So:

• في المطبخ ثلاجة كبيرة literally looks like
• In the kitchen, a big refrigerator

but it naturally means

• There is a big refrigerator in the kitchen

Arabic can express this idea without an explicit verb.
If you want a more explicit version, you could say:

• توجد ثلاجة كبيرة في المطبخ

But the original sentence is very normal and natural.

المطبخ has الـ because it means the kitchen — a specific, known place.

ثلاجة is indefinite because the sentence is introducing it as a refrigerator, not the refrigerator.

This is very common in Arabic existential sentences:

• في الغرفة سرير
• There is a bed in the room

If you said الثلاجة instead, you would be talking about a specific refrigerator already known in the conversation.

In Arabic, adjectives usually come after the noun they describe.

So:

• ثلاجة كبيرة = a big refrigerator

not:

• كبيرة ثلاجة

This is the normal noun + adjective order in Arabic.

More examples:

• بيت كبير = a big house
• سيارة جديدة = a new car

Because ثلاجة is a feminine noun, and Arabic adjectives must agree with the noun they describe.

So:

• ثلاجة = feminine singular
• كبيرة = feminine singular

If the noun were masculine, you would use كبير:

• مطبخ كبير = a big kitchen

Arabic adjectives agree in:

• gender
• number
• definiteness

وفيها is made of two parts:

• و = and
• فيها = in it

So:

• وفيها ماء وفاكهة literally means
• And in it, water and fruit

Natural English:

• And it has water and fruit
• And in it there is water and fruit

The ها means it (feminine), and it refers to ثلاجة.

That makes sense because ثلاجة is feminine in Arabic.

So:

• فيها = in it
• here, it = the refrigerator

If it referred to a masculine noun, Arabic would use فيه instead.

For example:

• المطبخ كبير وفيه نافذة
• The kitchen is big, and it has a window

Here فيه refers to المطبخ, which is masculine.

Because they are also being mentioned in a general, non-specific way:

• ماء = water
• فاكهة = fruit

The sentence is not talking about some specific known water or specific known fruit. It is simply saying that the refrigerator contains those things.

This is very natural in Arabic after an expression like فيها.

Because فاكهة in Arabic can work like a collective/general noun, much like English fruit.

So:

• فاكهة = fruit in a general sense

If you want an actual plural meaning like fruits, Arabic can also use:

• فواكه

But in a sentence like this, فاكهة is completely normal.

In fully vocalized, careful MSA, it would be:

• في المطبخِ ثلّاجةٌ كبيرةٌ، وفيها ماءٌ وفاكهةٌ.

A few things are happening here:

• المطبخِ is after the preposition في, so it is in the genitive
• ثلّاجةٌ is the delayed subject/topic of the existential structure, so it is nominative
• كبيرةٌ matches ثلّاجةٌ
• ماءٌ and فاكهةٌ are also nominative in this structure

In normal printed Arabic, these endings are usually not written, and in pause they are often not pronounced.

Yes. For example:

• هناك ثلاجة كبيرة في المطبخ
• توجد ثلاجة كبيرة في المطبخ

Both can mean There is a big refrigerator in the kitchen.

But في المطبخ ثلاجة كبيرة is a very common and natural MSA way to say it. It is simple and idiomatic.

Because the two و's are doing different jobs.

• و in وفيها connects the second clause to the first: and
• و in ماء وفاكهة joins two nouns: water and fruit

So the sentence structure is:

• ... and in it [there is] water and fruit

This repetition of و is completely normal in Arabic.