Chcę zgłosić problem.

Chcę means I want.

It is the 1st person singular present-tense form of the verb chcieć = to want.

So:

• chcę = I want
• chcesz = you want
• chce = he/she/it wants

The ending -ę is a very common ending for I forms in Polish verbs.

After chcę (I want), Polish usually uses another verb in the infinitive, just like English uses to + verb:

• Chcę zgłosić problem. = I want to report a problem.

So the structure is:

• chcę
  • infinitive

Examples:

• Chcę iść. = I want to go.
• Chcę zadzwonić. = I want to call.
• Chcę zgłosić problem. = I want to report a problem.

In Polish, the infinitive does not need a separate word like English to.

English:

• to report

Polish:

• zgłosić

So zgłosić already means to report as a dictionary form.

That is why Chcę zgłosić problem is natural, and you do not add another word for to.

Zgłosić means to report, to notify, or to submit something formally.

In this sentence, it suggests reporting a problem to a company, office, support desk, teacher, app, or authority.

Typical uses:

• zgłosić problem = report a problem
• zgłosić błąd = report a bug/error
• zgłosić reklamację = file a complaint / make a claim
• zgłosić się = report oneself / come forward / apply
  
  • This is a different construction because of się.

This is a very common Polish question because it involves aspect.

• zgłosić = perfective
• zgłaszać = imperfective

In simple terms:

• zgłosić focuses on completing the action: to report
• zgłaszać focuses on the process, repetition, or habit: to be reporting / to report regularly

So:

• Chcę zgłosić problem. = I want to report a problem.
  This means a single completed act of reporting.

Compare:

• Chcę zgłaszać problemy na bieżąco. = I want to report problems regularly / as they come up.

In your sentence, zgłosić is the natural choice.

Because problem is the direct object of the verb zgłosić, so it is in the accusative case.

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

So:

• nominative: problem
• accusative: problem

That is why the sentence uses:

• zgłosić problem

not:

• zgłosić problemu
• zgłosić problemem

Those would be wrong here.

A learner-friendly approximation is:

• Chcę ≈ h-tsen or kht-sen
• zgłosić ≈ z-gwoh-sheetch
• problem ≈ pro-blem

A few pronunciation notes:

• ch sounds like a hard h sound
• c sounds like ts
• ę is a nasal vowel, but in everyday speech its exact pronunciation depends on the sound after it
• ł sounds like English w
• ś sounds like a soft sh
• ć sounds like a soft ch

The first word, chcę, is especially tricky for English speakers because of the consonant cluster.

No, Polish word order is fairly flexible, but Chcę zgłosić problem is the most neutral and natural order.

You might also hear:

• Problem chcę zgłosić.
• Zgłosić chcę problem.

But these sound marked, emphatic, or context-dependent.

For a learner, the best default is:

• Chcę zgłosić problem.

That is the normal, clear way to say it.

It is neutral and works well in many situations.

You could use it:

• in customer service
• in an email
• in a help desk chat
• at a reception desk
• in a public office

It is polite enough on its own, but in a more formal situation you might add something like:

• Chciałbym zgłosić problem. = I would like to report a problem.
  said by a man
• Chciałabym zgłosić problem. = I would like to report a problem.
  said by a woman

These sound a bit softer and more polite than Chcę zgłosić problem.

Both are correct, but they differ in tone.

• Chcę zgłosić problem. = I want to report a problem.
• Chciałbym zgłosić problem. = I would like to report a problem.
  masculine speaker
• Chciałabym zgłosić problem. = I would like to report a problem.
  feminine speaker

Chcę is more direct. Chciałbym / Chciałabym is more polite, softer, and often better in service or formal contexts.

Sometimes, yes, but they are not always exact substitutes.

• problem = problem / issue
  the most general and safest choice
• kłopot = trouble / difficulty
  more everyday and a bit less formal in some contexts
• sprawa = matter / issue / case
  broader and not always the same thing
• usterka = fault / malfunction
  especially for technical or mechanical problems

So if you are talking generally, problem is the best default.

Examples:

• Chcę zgłosić problem z aplikacją. = I want to report a problem with the app.
• Chcę zgłosić usterkę. = I want to report a fault.
  better for equipment or a device

Yes, very often you will.

A common pattern is:

• zgłosić problem z + instrumental

Examples:

• Chcę zgłosić problem z internetem. = I want to report a problem with the internet.
• Chcę zgłosić problem z kontem. = I want to report a problem with the account.
• Chcę zgłosić problem z płatnością. = I want to report a problem with the payment.

Notice that after z in this meaning, Polish uses the instrumental case:

• internet → internetem
• konto → kontem
• płatność → płatnością

Yes. Chcę zgłosić problem. is a complete, natural sentence.

It has:

• the subject built into the verb: chcę = I want
• an infinitive verb: zgłosić
• an object: problem

Polish often leaves out pronouns like ja (I) because the verb form already shows the person.

So:

• Ja chcę zgłosić problem.

is possible, but usually you would only say ja for emphasis. The normal version is simply:

• Chcę zgłosić problem.