A fogorvos fúrja az őrlőfogat.

• A fogorvos = the dentist. This is the subject.
• fúrja = drills / is drilling it. This is the verb.
• az őrlőfogat = the molar. This is the direct object.

So the structure is basically:

[subject] + [verb] + [object]

They are the same word, just used in different sound environments:

• a before a consonant
• az before a vowel

So:

• a fogorvos because fogorvos starts with f
• az őrlőfogat because őrlőfogat starts with ő

This is a bit like English a/an, except in Hungarian it is the definite article the that changes form.

Yes. Hungarian very often makes compound nouns.

• fogorvos = fog

  • orvos
    literally tooth-doctor = dentist

• őrlőfog = őrlő

  • fog
    literally grinding tooth = molar

So both are normal Hungarian compound words.

A very important clue is the accusative ending on the object.

• a fogorvos has no object ending, so it is the subject
• az őrlőfogat has the accusative ending, so it is the object

In English, word order usually tells you this. In Hungarian, case endings help a lot.

So even if word order changes, the ending on őrlőfogat still tells you that it is the thing being drilled.

Because it is the direct object, and Hungarian marks direct objects with the accusative.

The dictionary form is:

• őrlőfog = molar

As an object, it becomes:

• őrlőfogat = molar
  • accusative

The important ending is -t, but many Hungarian nouns insert a linking vowel before that ending. So here it is not just -t, but -at.

Compare:

• őrlőfog → őrlőfogat

So the sentence uses őrlőfogat because the dentist is acting on the molar.

Because Hungarian has two kinds of verb conjugation:

• indefinite conjugation
• definite conjugation

Here the object is definite: az őrlőfogat = the molar, a specific molar.
So Hungarian uses the definite verb form:

• fúrja

If the object were not definite, you would use the indefinite form:

• A fogorvos fúr egy őrlőfogat. = The dentist is drilling a molar.
• A fogorvos fúr. = The dentist is drilling.

So:

• fúr = used without a definite object
• fúrja = used with a definite object

It can mean either, depending on context.

Hungarian present tense often covers both:

• simple present: drills
• present continuous: is drilling

So this sentence could be understood as:

• The dentist drills the molar or
• The dentist is drilling the molar

In most real situations, English would probably choose is drilling.

No, Hungarian word order is flexible, but it is not random. Changing the order usually changes the emphasis.

The version you have:

• A fogorvos fúrja az őrlőfogat.

is a normal, straightforward sentence.

If you move things around, you can highlight different parts. For example:

• A fogorvos az őrlőfogat fúrja.

This puts extra focus on the molar.

So the original order is a good neutral pattern for learners, but Hungarian can rearrange elements for topic and focus.

Yes, very often.

Hungarian often omits subject pronouns because the verb ending already shows the person. So if the context is clear, you could say:

• Fúrja az őrlőfogat.

This means:

• He/She is drilling the molar.

But if you want to say specifically that the dentist is the one doing it, then you keep:

• A fogorvos fúrja az őrlőfogat.

So Hungarian often drops pronouns, but it keeps a noun subject when that information matters.