Javni bilježnik radi danas.

Yes. Javni bilježnik is the standard Croatian term for a notary public.

Literally:

• javni = public
• bilježnik = notary / recorder / official who certifies documents

As a fixed expression, javni bilježnik means the legal profession, not just any “public note-taker.”

Because this is the subject of the sentence, so it is in the nominative singular.

• javni = nominative singular masculine form of the adjective
• bilježnik = nominative singular masculine noun

The sentence is basically:

• Javni bilježnik = the notary public
• radi = works / is working
• danas = today

If the noun changed case, the adjective would normally change with it.

Because javni agrees with bilježnik, which is a masculine singular noun in the nominative.

In Croatian, adjectives change form to match the noun’s:

• gender
• number
• case

So javni is the correct matching form for bilježnik here.

It can mean either, depending on context.

In this sentence, radi danas most naturally means:

• is working today or
• is on duty / is open today

Croatian present tense often covers both:

• a general present: works
• a current/temporary present: is working

English usually forces you to choose, but Croatian often does not.

Because radi is a full verb meaning works / is working. It is not an adjective or noun phrase that would need a form of to be.

So:

• Javni bilježnik radi danas. = The notary is working today.

Croatian does have forms of to be (biti), but they are not needed here.

Yes. Croatian word order is fairly flexible.

These are all possible:

• Javni bilježnik radi danas.
• Danas javni bilježnik radi.
• Javni bilježnik danas radi.

They all mean roughly the same thing, but the emphasis changes slightly.

For example:

• Danas javni bilježnik radi. puts more focus on today
• Javni bilježnik danas radi. is also very natural and common

The version you were given is completely correct.

In context, it usually means something specific about today:

• the notary is working today
• the notary is available today
• the office is open today

Without context, radi can simply mean works, but adding danas strongly suggests a temporary situation for today.

Croatian does not have articles like English a/an/the.

So javni bilježnik can mean:

• a notary public
• the notary public

The exact meaning depends on context.

In this sentence, English will usually translate it as The notary public is working today or A notary public is working today, depending on the situation.

The dictionary form is raditi, meaning to work.

Radi is the 3rd person singular present tense form:

• ja radim = I work / am working
• ti radiš = you work / are working
• on/ona/ono radi = he/she/it works / is working

So javni bilježnik radi literally means the notary works / is working.

Raditi is imperfective.

That matters because imperfective verbs are the normal choice for:

• ongoing actions
• habitual actions
• general present-tense statements

So radi danas fits naturally for is working today.

A rough pronunciation guide:

• bilježnik ≈ BEE-lyezh-neek
• radi ≈ RAH-dee
• javni ≈ YOW-vnee
• danas ≈ DAH-nahs

A few useful sound notes:

• j is pronounced like English y
• ž sounds like the s in measure
• lj is a single sound, somewhat like lli in million for many learners

Yes, bilježnik is a masculine singular noun.

That is why the adjective appears as javni, not a feminine or neuter form.

You can often recognize masculine nouns in Croatian by their dictionary form ending in a consonant, as bilježnik does.

Possibly in some contexts, but javni bilježnik is the standard Croatian legal term for notary public.

If your goal is standard, correct Croatian for the profession, javni bilježnik is the safest and most natural choice.

Yes, it is natural and correct.

A very common alternative word order would be:

• Javni bilježnik danas radi.

That version may sound slightly more neutral in everyday speech, but your original sentence is perfectly fine.