Я чую дверний дзвінок і думаю, що це Олена.

Because чути means to hear, while слухати means to listen.

• чути = noticing a sound
• слухати = actively paying attention to a sound

So Я чую дверний дзвінок means you hear the doorbell, not that you are intentionally listening to it.

It is in the accusative case, because it is the direct object of чую.

However, for a masculine inanimate noun like дзвінок, the accusative singular looks exactly the same as the nominative singular. So:

• nominative: дверний дзвінок
• accusative: дверний дзвінок

That is why the form does not visibly change.

Дверний is an adjective meaning door- or related to a door.

So:

• двері = door / doors
• дверний = door-, as an adjective

Ukrainian often uses an adjective where English uses a noun modifier.
So дверний дзвінок literally means something like door bell, which is the normal way to say doorbell.

Here дзвінок means a ring or bell sound, and with дверний it means doorbell.

This word can mean different but related things in other contexts, for example:

• телефонний дзвінок = a phone call
• дзвінок = a ring / bell / call

So the adjective дверний makes the meaning clear.

Що means that and introduces the clause after думаю.

So:

• думаю, що... = I think that...

In English, that is often optional: I think it’s Olena.
In Ukrainian, що is very common and natural in this kind of sentence.

Because after це in an identification sentence, Ukrainian normally uses the nominative form.

So:

• Це Олена. = It is Olena.
• Це мій брат. = This is my brother.

You are identifying who the person is, not using the name as a direct object, so Олена stays in the nominative.

Because the same subject applies to both verbs:

• Я чую ... і думаю ...

Ukrainian does not need to repeat the pronoun if it is already clear. The verb endings also help:

• чую = I hear
• думаю = I think

You could repeat я for emphasis, but it is not necessary.

Because Ukrainian does not have articles like a and the.

So whether something is a doorbell or the doorbell is understood from context. That is normal in Ukrainian.

They are both present tense forms:

• чую = I hear
• думаю = I think

They are also imperfective verbs, which is what you normally use here for an action or state happening now.

Yes. Ukrainian word order is fairly flexible, and changing it usually changes emphasis, not the basic meaning.

The given sentence is neutral and natural:

• Я чую дверний дзвінок і думаю, що це Олена.

But you could also say:

• Чую дверний дзвінок і думаю, що це Олена.

This sounds a bit more conversational, because Ukrainian often drops я when it is obvious.

The main stress is:

• чу́ю
• дверни́й
• дзвіно́к
• ду́маю
• Оле́на

So the sentence is:

Я чу́ю дверни́й дзвіно́к і ду́маю, що це Оле́на.