A szerző könyvet ír.

No. In Hungarian, a here means the, not English a/an.

• a szerző = the author
• Hungarian has two forms of the definite article:
  • a before a consonant sound
  • az before a vowel sound

Since szerző starts with sz, which is a consonant sound, the sentence uses a szerző.

The Hungarian word for English a/an is egy, but Hungarian often leaves egy out in sentences like this.

Because könyvet is the accusative form, used for a direct object.

• könyv = book
• könyvet = book, as the thing being written

Hungarian usually marks direct objects with -t. In this word, an extra vowel appears before the -t for easier pronunciation:

• könyv + t would be awkward
• so Hungarian uses könyvet

So the -t shows that the book is what the author is writing.

Hungarian often leaves out the indefinite article egy when English would use a/an, especially with an indefinite, nonspecific object.

So:

• A szerző könyvet ír. can mean The author writes a book or The author is writing a book
• A szerző egy könyvet ír. also works, but it makes the one book / a book idea more explicit

If the book were definite, Hungarian would normally use the definite article:

• A szerző írja a könyvet. = The author is writing the book

Hungarian has two main verb conjugation patterns:

• indefinite conjugation
• definite conjugation

Here the object is indefinite: könyvet = a book / book, not the book. Because of that, the verb uses the indefinite form:

• ír = he/she writes

If the object were definite, the verb would usually switch to the definite form:

• írja = he/she writes it / writes the specific thing

Compare:

• A szerző könyvet ír. = The author writes/is writing a book.
• A szerző írja a könyvet. = The author is writing the book.

Hungarian often makes this clear through case marking, not just word order.

• szerző has no object ending, so it is the subject
• könyvet has the accusative ending -t, so it is the object

That means:

• the author is doing the action
• the book is receiving the action

This is one reason Hungarian can have more flexible word order than English.

It can mean either, depending on context.

Hungarian present tense often covers both:

• a general or habitual meaning: writes
• a current ongoing meaning: is writing

So A szerző könyvet ír. could mean:

• The author writes a book
• The author is writing a book

In real use, context usually makes the intended meaning clear. Hungarian does not have a separate compulsory progressive form like English is writing.

Yes, the word order can change. Hungarian word order is much more flexible than English word order, and it is strongly connected to topic and focus.

In A szerző könyvet ír:

• A szerző is the topic: we are talking about the author
• könyvet ír says what the author does

With an indefinite object like könyvet, putting it before the verb is very natural.

Other word orders are possible, but they usually change the emphasis rather than the basic meaning.

A few very important Hungarian spelling points appear in this sentence:

• sz is pronounced like English s in see
• ny is a soft sound similar to Spanish ñ
• í is a long vowel
• ő is also a long vowel, and it has no exact English equivalent

So the accents are not optional decoration: they show real sound differences, especially vowel length and quality.

That means:

• ír is not the same as ir
• szerző is not the same as szerzo

In Hungarian, these differences matter for correct pronunciation and sometimes for meaning too.