أخصائي صحة الأسنان قرب كرسي الأسنان.

Because this is a nominal sentence in Arabic. In the present tense, Arabic normally leaves out the verb to be.

So:

أخصائي صحة الأسنان قرب كرسي الأسنان
literally has the structure:

• أخصائي صحة الأسنان = the dental hygienist / dental-health specialist
• قرب كرسي الأسنان = near the dental chair

In natural English, you add is, but Arabic does not need it here.

Literally, it breaks down like this:

• أخصائي = specialist
• صحة الأسنان = health of the teeth, or dental health

So the whole phrase is literally something like specialist of dental health. In normal English, that is often rendered as dental hygienist or oral-health specialist, depending on context.

Yes. It is a single noun phrase built with إضافة (the construct state).

More exactly, it is a chain:

• صحة الأسنان = health of the teeth
• أخصائي صحة الأسنان = specialist of the health of the teeth

Arabic very often links nouns this way instead of using of or an adjective the way English does.

Because in an إضافة construction, the first noun does not take ال.

So Arabic says:

• أخصائي صحة الأسنان not
• الأخصائي صحة الأسنان

The definiteness comes from the end of the phrase. Since الأسنان is definite, the whole chain becomes definite.

The same thing happens in:

• صحة الأسنان
• كرسي الأسنان

In both of those, the first word also appears without الـ.

Because صحة ends in ة (tāʾ marbūṭa).

When a word ending in ة is said by itself in pause, it usually sounds like -a / -ah. But when it is linked to another word in إضافة, the t sound appears.

So:

• by itself: صحة ≈ ṣiḥḥa
• in the phrase: صحة الأسنان ≈ ṣiḥḥat al-asnān

This is very common in Arabic.

Here قرب means near or close to.

Grammatically, it is often treated as a ظرف (an adverbial expression of place), and it is followed by a noun phrase:

• قرب كرسي الأسنان = near the dental chair

So the sentence is saying that the dental hygienist is located near the chair.

You may also see similar expressions such as:

• قريب من = near
• بالقرب من = near / close to

But قرب is a compact and very common way to say it.

Because Arabic naturally says teeth in expressions like this:

• صحة الأسنان = dental health
• كرسي الأسنان = dental chair

English often uses an adjective like dental, but Arabic often uses a noun phrase instead. So using the plural الأسنان is normal and idiomatic here.

Also, الأسنان is the plural of سِنّ or سَنّ depending on usage and vocalization.

Because Arabic often expresses this kind of idea with noun + noun rather than adjective + noun.

So:

• كرسي الأسنان literally = chair of the teeth / dentistry
• natural meaning = dental chair

This is another إضافة construction, just like صحة الأسنان.

So yes, it sounds more literal if you translate word-for-word, but it is a perfectly normal Arabic way to build the phrase.

In careful grammar, the noun phrases here are definite because they end in definite nouns:

• أخصائي صحة الأسنان → definite because صحة الأسنان is definite
• صحة الأسنان → definite because الأسنان is definite
• كرسي الأسنان → definite because الأسنان is definite

So grammatically, the sentence is closer to:

The dental hygienist is near the dental chair.

That said, beginner materials sometimes translate more loosely depending on context.

Yes. The order here is very natural:

• أخصائي صحة الأسنان = topic / subject
• قرب كرسي الأسنان = predicate / location

But Arabic can move the location phrase to the front for emphasis:

• قرب كرسي الأسنان أخصائي صحة الأسنان

That would mean something like:

Near the dental chair is the dental hygienist.

So the original order is the neutral one, but other orders are possible.

You would usually use the feminine job title:

أخصائية صحة الأسنان قرب كرسي الأسنان.

So:

• أخصائي = male specialist
• أخصائية = female specialist

Job titles in Arabic often match the gender of the person being described.