Ha a kutya ugat és kaparja az ajtót, akkor megnézem.

Ha means if, and akkor means then.

So the structure is:

Ha ..., akkor ... = If ..., then ...

In Hungarian, akkor is often optional. You could say:

Ha a kutya ugat és kaparja az ajtót, megnézem.

That still sounds natural. Adding akkor just makes the if-then relationship more explicit.

Hungarian has two forms of the definite article:

• a before a consonant
• az before a vowel

So:

• a kutya = the dog because kutya starts with k
• az ajtót = the door because ajtó starts with a vowel

This is similar to how English uses a and an, but in Hungarian it happens with the definite article the.

Because ajtót is the direct object of the verb kaparja.

Hungarian marks many direct objects with the accusative ending -t:

• ajtó = door
• ajtót = door, as a direct object

So:

kaparja az ajtót = scratches the door

The article stays az, and the noun gets the object ending:

• az ajtó = the door
• az ajtót = the door, as the thing being scratched

Because Hungarian verbs have two kinds of conjugation:

• indefinite conjugation
• definite conjugation

When the verb has a definite direct object, Hungarian usually uses the definite conjugation.

Here the object is az ajtót = the door, which is definite, so the verb becomes:

• kapar = he/she scratches, with no definite object or with an indefinite one
• kaparja = he/she scratches it / scratches the definite object

So:

• A kutya kapar. = The dog is scratching.
• A kutya kaparja az ajtót. = The dog is scratching the door.

For the same reason: this is also the definite conjugation.

• megnézek = I look at / check something indefinite
• megnézem = I look at / check it, or some definite thing

In this sentence, the object is not stated directly, but it is understood from context. The speaker means something like I’ll check it / I’ll go see.

Hungarian often leaves the object unstated if it is obvious. Even so, the verb can still appear in the definite form.

Meg- is a verbal prefix. Here it gives the verb a more completed, goal-oriented meaning.

Compare:

• nézem = I am looking at it / watching it
• megnézem = I’ll check it / I’ll go and have a look / I’ll take a look

So megnézem does not just mean I see in a general sense. It suggests a complete action: the speaker will go check what is happening.

Hungarian very often uses the present tense to talk about the future when the context makes the time clear.

Here the conditional structure already tells you this is about a future or possible situation:

Ha a kutya ugat és kaparja az ajtót, akkor megnézem.

Literally, the last verb is present tense, but in natural English it is often best translated as:

• I’ll check
• I’ll go see
• I’ll take a look

So this is normal Hungarian usage, not a mistake.

In a neutral statement, the verbal prefix usually stays attached to the verb:

• megnézem

But the prefix often separates when the verb is negated, focused, or put into certain other structures.

For example:

• Megnézem. = I’ll check it.
• Nem nézem meg. = I won’t check it.
• Csak akkor nézem meg, ha muszáj. = I only check it then if I have to.

So in your sentence, akkor megnézem is a normal neutral order, and the prefix stays attached.

No. This sentence uses a direct-object structure:

• kaparja az ajtót = scratches the door

Hungarian can also use a structure more like scratch on the door, for example:

• az ajtón kapar

That shifts the wording a bit. The version in your sentence presents the door as the direct object of the scratching. English might translate both in similar ways, depending on context.

So the sentence you have is natural, but it is not the only possible way to express the idea.