Czy często korzystasz z tej aplikacji, czy wolisz zwykły zeszyt?

They do two different jobs here:

• The first czy marks the whole sentence as a yes/no question.
• The second czy means or when presenting an alternative.

So the structure is basically:

• Czy ... , czy ... ?
• Do you ... , or do you prefer ... ?

In English, we usually do not repeat whether/or in the same way, so this can feel unusual at first.

Because the verb korzystać requires the preposition z and the noun after it must be in the genitive case.

So:

• korzystać z czego? = to use / make use of what?
• z tej aplikacji = from/of this app in grammatical terms, though in natural English it simply means this app

That is why you get:

• ta aplikacja → nominative
• tej aplikacji → genitive after z

This is something learners usually just need to memorize with the verb:

• korzystać z internetu
• korzystać z telefonu
• korzystać z aplikacji

Because both words have to match the case required by z after korzystać.

Base form:

• ta aplikacja = this app

After z, it changes to genitive:

• tej aplikacji

So both the demonstrative adjective and the noun change:

• ta → tej
• aplikacja → aplikacji

This agreement is very important in Polish: adjectives, demonstratives, and nouns usually have to match in gender, number, and case.

Because woleć normally takes the accusative case, and zeszyt is a masculine inanimate noun.

For masculine inanimate nouns, the accusative singular is the same as the nominative singular.

So:

• nominative: zwykły zeszyt
• accusative: zwykły zeszyt

That is why nothing changes here.

Compare that with a masculine animate noun, where accusative would change:

• widzę dobrego nauczyciela
  not
• widzę dobry nauczyciel

Because Polish often omits subject pronouns when they are clear from the verb ending.

• korzystasz = you use / you are using
• wolisz = you prefer

Both verb forms already show you singular, so ty is unnecessary.

You could say:

• Czy ty często korzystasz z tej aplikacji...?

but that usually adds emphasis, contrast, or emotion. In neutral speech, Polish normally leaves ty out.

It refers to one person, in the informal singular form.

• korzystasz = you use / you are using addressed to one person informally
• wolisz = you prefer addressed to one person informally

If you were speaking to:

• more than one person: korzystacie, wolicie
• one person formally: often Czy pan/pani często korzysta... ?

So this sentence sounds like you are speaking to one person you address as ty.

Zeszyt usually means a notebook in the sense of a paper exercise book, school notebook, or writing pad made of bound pages.

It does not mean a laptop computer.

So in this sentence, zwykły zeszyt means something like:

• a regular notebook
• a normal paper notebook

The word zwykły emphasizes that it is an ordinary, traditional notebook, not an app or digital tool.

Często means often. It tells you about frequency.

In this sentence:

• Czy często korzystasz z tej aplikacji...?
• Do you often use this app...?

Its position can sometimes change, because Polish word order is more flexible than English, but not every version sounds equally natural.

Very natural:

• Czy często korzystasz z tej aplikacji...?

Possible, with different emphasis:

• Czy korzystasz często z tej aplikacji...?

The version in the original sentence is the most neutral and natural.

It can mean either, depending on context.

Polish present tense often covers both:

• you use
• you are using

Here, because of często (often), the meaning is clearly habitual:

• Do you often use this app...?

So it is not about what someone is doing right now at this exact moment.

Yes. In modern Polish, aplikacja is a normal and very common word for app or application, especially in technology contexts.

So:

• ta aplikacja = this app

In everyday speech, Polish speakers very commonly use aplikacja for mobile apps, learning apps, banking apps, and so on.

Not naturally in this exact structure.

The sentence:

• Czy często korzystasz z tej aplikacji, czy wolisz zwykły zeszyt?

presents two alternatives in a question: do you do X, or do you prefer Y?

Using czy for the second part is very natural here.

You might sometimes see other ways of expressing alternatives, but czy ... czy ... is a standard and elegant way to frame this kind of question.

Also note:

• albo and lub are more like plain or
• czy works especially well in questions and alternative choices

A few parts may be difficult for English speakers:

• czy — roughly like chy with a hard ch/sh-like sound at the start
• często — the cz sounds a bit like ch in church, but harder; ę is nasal
• korzystasz — watch the rz sound, which is pronounced like ż
• zeszyt — pronounced roughly ZE-shit but with Polish vowels and consonants, so be careful not to anglicize it too much

Useful sound notes:

• cz = a hard ch-like sound
• sz = sh
• rz/ż = like the s in measure or zh

If you want to sound natural, zeszyt and korzystasz are especially worth practicing.

Polish word order is relatively flexible, but the original version is the most neutral and natural:

• Czy często korzystasz z tej aplikacji, czy wolisz zwykły zeszyt?

You can move elements around for emphasis, but that changes the feel:

• Czy z tej aplikacji często korzystasz, czy wolisz zwykły zeszyt?
  This puts more focus on this app.

• Czy zwykły zeszyt wolisz, czy często korzystasz z tej aplikacji?
  Grammatically possible in a special context, but much less natural as a neutral question.

So yes, word order can vary, but the original sentence is the best default model to learn.