Po pločniku piše kredom svoje ime i smije se.

Here po means something like over, along, or across the surface of.

So po pločniku piše suggests that the person is writing on the pavement surface.

This preposition commonly takes the locative case, which is why you get pločniku.

A useful contrast:

• na pločniku = on the pavement/sidewalk as a location
• po pločniku = over/across the pavement, often emphasizing movement or action spread over the surface

In this sentence, po sounds natural because writing with chalk happens on the surface of the pavement.

Because po normally requires the locative case.

The noun pločnik is masculine singular:

• nominative: pločnik
• locative: pločniku

So:

• pločnik = the pavement/sidewalk
• po pločniku = on/over the pavement

This is a very common pattern in Croatian: the preposition controls the case of the noun after it.

Piše is present tense, 3rd person singular, from the verb pisati = to write.

It can mean:

• writes
• is writing

Croatian present tense often covers both the simple present and the English present continuous, depending on context.

So piše here can naturally be understood as is writing.

Because kredom is the instrumental singular of kreda = chalk.

The instrumental case is often used for the means or tool used to do something.

So:

• kreda = chalk
• kredom = with chalk

This is exactly the same idea as in English with chalk.

Svoje ime is the direct object of piše, so it is in the accusative.

• svoje = accusative singular neuter of svoj
• ime = a neuter noun; its nominative and accusative singular look the same

So:

• nominative: svoje ime
• accusative: svoje ime

Even though the form looks unchanged, the function here is accusative because it answers what is she/he writing?
Answer: svoje ime.

Because Croatian usually uses the reflexive possessive svoj when the possessor is the same as the subject.

So if the subject is the one writing their own name, Croatian prefers:

• piše svoje ime = writes his/her own name

Using njegovo ime or njezino ime would more strongly suggest someone else’s interpretation or would sound less natural if it refers back to the subject.

A good rule:

• use svoj when the owner = the subject of the clause
• use njegov / njezin / njihov when the owner is someone else

The subject is not stated explicitly, but it is still there grammatically.

Both piše and smije se are 3rd person singular, so the sentence means:

• he is writing ... and laughing or
• she is writing ... and laughing

Croatian often leaves out subject pronouns like on or ona when the verb form already makes the person and number clear.

This is very normal and very common.

Smije se means laughs or is laughing.

The full verb is smijati se = to laugh.

This is important because se is part of the verb here. You should learn it as a unit:

• smijati se = to laugh
• smije se = he/she laughs, is laughing

Do not confuse this with smjeti, which means to be allowed to / may.
For example:

• On se smije. = He is laughing.
• On smije ići. = He may go.

Those are different verbs.

Because se is a clitic, and Croatian clitics have special word-order rules.

In practice, learners should usually remember that se often comes very early in its clause, but it also commonly appears right after the verb in simple sentences like this:

• smije se

Since this is the second clause after i, the form i smije se is perfectly natural.

So the main thing to remember is:

• the verb is smijati se
• in the present tense, you normally say smije se

Because Croatian, like English, can join two actions with i = and.

The sentence has two coordinated actions:

• piše kredom svoje ime
• smije se

Both actions have the same implied subject, so there is no need to repeat it.

This works just like English:

• He writes his name in chalk and laughs.

Croatian simply leaves out he/she because the verb forms already show that there is one 3rd-person singular subject.

Yes, but the meaning would shift slightly.

• na pločniku piše kredom svoje ime = he/she is writing on the pavement, focusing more on location
• po pločniku piše kredom svoje ime = he/she is writing over/across the pavement surface, which sounds especially natural for chalk writing

So po pločniku is a good choice here because it matches the idea of writing on the surface of the sidewalk.

Croatian word order is fairly flexible, though not completely free.

The sentence:

• Po pločniku piše kredom svoje ime i smije se.

is natural and neutral enough in context.

You could also rearrange parts for emphasis, for example:

• Kredom piše svoje ime po pločniku i smije se.
• Svoje ime piše kredom po pločniku i smije se.

These versions are still understandable, but they shift the emphasis slightly.

So the original order is not the only possible one, but it is a normal Croatian sentence.