Ha korán hazaérek, még olvasok egy kicsit.

Ha means if. It introduces a condition:

• Ha korán hazaérek = If I get home early

It works very much like English if in this kind of sentence.

Hungarian often uses the present tense for future meaning when the context already makes the time clear.

So:

• hazaérek literally looks like I get home / I arrive home
• olvasok literally looks like I read

But in this sentence they naturally mean:

• If I get home early, I’ll read a little

This is especially common:

• in if-clauses
• when the future is obvious from the situation
• in everyday speech

Using a future form with fog is possible, but here the plain present is more natural.

Hazaérek is made up of:

• haza = homeward / to home
• érek = I arrive / I reach from érni

Together, hazaérek means:

• I get home
• I arrive home

So it is not just I arrive in general; it specifically includes the idea of home.

Because haza functions as a verbal prefix / directional element with the verb érek.

When that prefix stands directly before the verb, Hungarian writes it together:

• hazaérek = I get home

But this kind of prefix can separate in other sentence patterns, for example with negation or strong focus:

• Nem érek haza korán. = I don’t get home early.
• Korán érek haza. = I get home early. / It’s early that I get home.

So the one-word spelling is normal in the form used here.

This is a very common question.

• haza is about movement toward home
• otthon is about being at home

So:

• hazaérek = I get home
• otthon vagyok = I am at home

You would not use otthon inside hazaérek, because this sentence is about arriving home, not simply being there.

Because korán is the adverb meaning early, while korai is an adjective meaning early.

Here it modifies the verb hazaérek, so Hungarian needs the adverb:

• korán hazaérek = I get home early

Compare:

• korai vonat = an early train
• korán jövök = I come early

So:

• korai describes a noun
• korán describes an action

Because Ha korán hazaérek is a subordinate clause, and Hungarian normally separates that from the main clause with a comma.

So the structure is:

• Ha korán hazaérek, = conditional clause
• még olvasok egy kicsit. = main clause

This is standard Hungarian punctuation.

Here még adds the idea of:

• still
• yet
• in addition
• there will still be time to

So még olvasok egy kicsit is not just I read a little, but more like:

• I’ll still read a little
• I’ll have time to read a little too

If you remove még, the sentence is still grammatical, but it loses that extra nuance of still / additionally.

Because Hungarian has two conjugations here:

• indefinite: used when there is no definite object
• definite: used when there is a definite object

In this sentence, there is no definite thing being read. The sentence just says that the speaker will do some reading.

So Hungarian uses:

• olvasok = indefinite

You would use olvasom if there were a definite object, for example:

• Olvasom a könyvet. = I am reading the book.

Egy kicsit means a little bit or for a little while.

In this sentence it works adverbially, so it tells you how much / for a short amount of time the person will read:

• olvasok egy kicsit = I’ll read a bit

It is not really a definite object like the book or the newspaper. That is one reason the verb stays in the indefinite form olvasok.

Also, in everyday Hungarian, kicsit by itself is very common too:

• olvasok kicsit
• olvasok egy kicsit

Both are possible, though egy kicsit sounds a bit fuller and very natural here.

Yes, you could. It is a valid sentence.

But the word order changes the emphasis a little:

• Ha korán hazaérek = more neutral
• Ha korán érek haza = stronger focus on korán

So the version in your sentence is a very natural, neutral way to say it. The alternative is also common, but it can sound a bit more contrastive, as if the important point is specifically early.