Posiadacz rachunku używa bankowości elektronicznej.

A word-by-word breakdown:

• posiadacz = holder, owner, possessor
• rachunku = of an account
• używa = uses
• bankowości elektronicznej = electronic banking / online banking

So the structure is roughly:

• Posiadacz rachunku = the holder of an account
• używa bankowości elektronicznej = uses electronic banking

This is a fairly formal sentence.

Because rachunku is in the genitive case.

The base form is:

• rachunek = account, bill

But after another noun like posiadacz when you mean holder of an account, Polish usually uses the genitive:

• posiadacz rachunku = account holder
  literally: holder of account

This is very common in Polish:

• numer telefonu = phone number
• właściciel domu = owner of a house
• posiadacz rachunku = holder of an account

So rachunek changes to rachunku because it depends on posiadacz.

Because the verb używać takes the genitive case, not the accusative.

The dictionary form is:

• bankowość elektroniczna = electronic banking

But after używać:

• używać bankowości elektronicznej = to use electronic banking

So both words change into the genitive singular:

• bankowość → bankowości
• elektroniczna → elektronicznej

This is one of the most important things to remember in this sentence.

Yes, in standard Polish używać normally takes the genitive.

Examples:

• używać komputera = to use a computer
• używać telefonu = to use a phone
• używać bankowości elektronicznej = to use electronic banking

This often surprises English speakers, because in English use does not visibly change the noun, but in Polish the following noun must be in the genitive.

Because adjectives in Polish must agree with the noun they describe in:

• gender
• number
• case

The noun here is:

• bankowość — feminine singular

And because it is in the genitive singular, the adjective must also be in the genitive singular feminine:

• elektroniczna → nominative singular feminine
• elektronicznej → genitive singular feminine

So:

• bankowość elektroniczna = electronic banking
• używa bankowości elektronicznej = uses electronic banking

It is natural, but it sounds formal and is common in banking, legal, or administrative language.

In everyday speech, people might more often say:

• właściciel konta = account owner
• osoba, która ma konto = a person who has an account

Also note that in modern everyday Polish, konto is often more common than rachunek for a bank account, depending on context.

So:

• posiadacz rachunku = formal/institutional
• właściciel konta = more everyday

In banking contexts, both can relate to an account, but they are not always interchangeable in every situation.

Very roughly:

• rachunek bankowy = bank account
• konto bankowe = bank account

In everyday speech, konto is often very common.
In official banking language, rachunek is also extremely common.

So this sentence sounds like something you might read in a bank document:

• Posiadacz rachunku używa bankowości elektronicznej.

A more conversational version might be:

• Właściciel konta używa bankowości internetowej.

Yes. Polish word order is more flexible than English word order because case endings show the grammatical relationships.

The neutral order here is:

• Posiadacz rachunku używa bankowości elektronicznej.

But you could also see:

• Bankowości elektronicznej używa posiadacz rachunku.

That version puts more emphasis on bankowości elektronicznej.

Even though the word order can change, the original sentence is the most straightforward and neutral.

Polish has no articles like English a or the.

So posiadacz rachunku can mean:

• an account holder
• the account holder

Which one is meant depends on context.

That is completely normal in Polish.
You do not need to add a word for the.

A rough pronunciation guide:

• Posiadacz ≈ po-SHYA-dach
• rachunku ≈ ra-HOON-koo
• używa ≈ oo-ZHI-va
• bankowości ≈ ban-ko-VOSH-chee
• elektronicznej ≈ e-lek-tro-NEECH-nej

A few useful pronunciation notes:

• sz sounds like English sh
• cz sounds like English ch, but harder
• ż sounds like the s in measure
• ści often sounds roughly like shchi
• stress in Polish usually falls on the second-to-last syllable

Yes, and in many contexts it may sound even more natural.

Compare:

• używa bankowości elektronicznej = uses electronic banking
• korzysta z bankowości elektronicznej = makes use of / uses electronic banking

The verb korzystać z is very common when talking about services or facilities.

Examples:

• Korzystam z internetu. = I use the internet.
• Korzysta z bankowości elektronicznej. = He/She uses online banking.

So your original sentence is correct, but korzysta z is also a very useful alternative to learn.