Můj syn se směje na skluzavce, ale moje malá dcera někdy pláče, když čeká moc dlouho.

Because Czech possessive adjectives agree with the noun they describe.

• syn is masculine singular, so you use můj
• dcera is feminine singular, so you use moje (or má)

So:

• můj syn = my son
• moje malá dcera = my little daughter

Also, malá agrees with dcera, because dcera is feminine singular.

Yes. Both are correct.

For the feminine singular form of můj, Czech allows:

• má
• moje

So both of these work:

• má malá dcera
• moje malá dcera

Má is often shorter and a bit more common in everyday use, but moje is perfectly natural too.

Here, se is part of the verb smát se, which means to laugh.

So the basic dictionary form is:

• smát se = to laugh

In this sentence:

• směje se = is laughing / laughs

Important: here se does not mean himself. It is just a fixed part of the verb. Many Czech verbs work like this.

Because Czech verbs change form when they are conjugated, and sometimes the stem changes too.

The infinitive is:

• smát se

But the 3rd person singular present is:

• (on) se směje = he laughs / he is laughing

So this is not a direct, simple cut-and-paste from the infinitive. It is just the normal present-tense form of this verb.

This is something you often have to learn verb by verb:

• čekat → čeká
• plakat → pláče
• smát se → směje se

Because na can take different cases depending on meaning.

Here it expresses location: the son is on the slide / at the slide, not moving onto it.
With location, na takes the locative case.

• skluzavka = slide
• na skluzavce = on the slide

If it meant movement onto the slide, Czech would use the accusative:

• na skluzavku = onto the slide

So:

• je na skluzavce = he is on the slide
• jde na skluzavku = he is going onto the slide

Because after na in the meaning of location, the noun must be in the locative singular.

The noun is:

• skluzavka

Its locative singular form is:

• skluzavce

So:

• na skluzavce = on the slide

This kind of ending change is a normal part of Czech noun declension.

Because malá and dlouho do different jobs.

• malá is an adjective describing a noun: dcera
• dlouho is an adverb describing a verb: čeká

So:

• malá dcera = little daughter
• čeká dlouho = waits a long time / waits long

In Czech, adjectives agree with nouns in gender, number, and case.
Adverbs do not.

Here it means too long or for too long.

• moc can mean very, much, a lot, or sometimes too, depending on context.
• In this sentence, because the daughter cries as a result, moc dlouho is best understood as too long.

So:

• čeká moc dlouho = she waits too long / for too long

Because Czech word order is flexible, and adverbs like někdy often go before the verb they modify.

So:

• dcera někdy pláče = the daughter sometimes cries

That is a very natural order.

You could move někdy in some contexts, but the sentence would sound slightly different in emphasis. The version in your sentence is neutral and normal.

Here když means when or whenever.

It introduces a subordinate clause:

• když čeká moc dlouho = when she waits too long

In other contexts, když can sometimes be close to if, but in this sentence when/whenever is the most natural understanding.

Because Czech punctuation requires them here.

• ale joins two clauses:
  • Můj syn se směje na skluzavce
  • moje malá dcera někdy pláče

So a comma is used before ale.

• když introduces a subordinate clause:
  • když čeká moc dlouho

In Czech, subordinate clauses are normally separated by commas.

So both commas are standard and expected.

Because Czech does not have articles like English the and a/an.

So Czech simply says:

• můj syn
• malá dcera
• na skluzavce

and the exact sense of a/the is understood from context.

This is completely normal in Czech. English needs articles, but Czech does not.