فرن الخزف هنا.

Because this is a nominal sentence in Arabic. In the present tense, Arabic usually does not use a separate word for is / are.

So:

• فرن الخزف هنا = The ceramic kiln is here

The idea of is is understood automatically.

If you wanted a past or future meaning, Arabic would normally use a verb or another structure, but in the simple present, leaving out is is completely normal.

Because فرن الخزف is an iḍāfa (إضافة), often called a construct phrase.

In an iḍāfa:

• the first noun does not take الـ
• the second noun determines whether the whole phrase is definite or indefinite

So here:

• فرن = kiln / oven
• الخزف = the ceramics / the pottery / ceramic ware

Together:

• فرن الخزف = the kiln of the ceramics / the ceramic kiln

Since الخزف is definite with الـ, the whole phrase is definite.

It is an iḍāfa phrase:

• فرن = the first part, called المضاف
• الخزف = the second part, called المضاف إليه

This structure often corresponds to English of or to a noun used like an adjective.

Possible ways to understand it in English:

• the kiln of the pottery
• the pottery kiln
• the ceramic kiln

English usually chooses the most natural wording rather than translating word-for-word.

In an iḍāfa, the second noun is grammatically genitive.

So, in fully vowelled Arabic, this would be:

• فُرْنُ الخَزَفِ هُنَا

Notice:

• فُرْنُ = nominative
• الخَزَفِ = genitive after iḍāfa
• هُنَا = here

In normal modern writing, those case endings are usually not written, so you just see:

• فرن الخزف هنا

A careful full pronunciation would be:

• furnu l-khazafi hunā

In pause, which is how people often actually say it aloud, it is more like:

• furn al-khazaf hunā or
• furn ul-khazaf hunā

A few pronunciation notes:

• خ is a throaty sound, like the ch in Scottish loch or German Bach
• هنا is hunā, with stress usually on the second syllable: hu-NĀ

Yes. In this sentence:

• فرن الخزف = the topic / subject part
• هنا = the predicate, telling you the location

So the structure is basically:

• [The ceramic kiln] [here]
• natural English: The ceramic kiln is here

Arabic often uses adverbs of place like هنا as the predicate in sentences like this.

Yes, you can. That word order is possible, but the emphasis changes slightly.

• فرن الخزف هنا = The ceramic kiln is here
• هنا فرن الخزف = Here is the ceramic kiln / The ceramic kiln is here, right here

Starting with هنا gives the location more prominence.

Both are grammatical; the choice depends on what you want to emphasize.

الخزف usually refers to:

• ceramics
• pottery
• earthenware

So فرن الخزف could be understood in several close ways depending on context:

• ceramic kiln
• pottery kiln
• kiln for ceramics

The exact English wording depends on what is most natural in the situation.

Because Arabic does not need many words to make a full sentence.

This sentence has everything necessary:

• a noun phrase: فرن الخزف
• a location predicate: هنا

That is enough to form a complete present-tense statement in Arabic.

So even though it is only three written words, it is fully complete and natural.

Usually, no. In ordinary Modern Standard Arabic writing, short vowels and case endings are often omitted.

So you normally write:

• فرن الخزف هنا

If fully vowelled for learners or formal grammatical illustration, it could be written:

• فُرْنُ الخَزَفِ هُنَا

Learners should know the grammar behind the endings, but in everyday reading, you will often see the unvowelled form only.

Yes. فرن can mean:

• oven
• furnace
• kiln

The best translation depends on context. Because it is followed by الخزف, the meaning kiln is especially likely here, since ceramics and pottery are typically associated with kilns rather than ordinary ovens.