Djeca su pazila da ne stanu na puža dok su izlazila iz kuće.

Djeca is a special word in Croatian. It means children, and it refers to more than one person, but its agreement is not the same as a regular masculine plural noun.

In this kind of sentence:

• the auxiliary is plural: su
• the past participle is usually in the neuter plural form: pazila, izlazila

So:

• Djeca su pazila
• Djeca su izlazila

This is standard Croatian. You would not normally say Djeca su pazili here.

Croatian often uses da + present tense where English uses an infinitive.

Here, paziti da... means something like:

• to be careful that...
• to make sure that...
• in natural English, to be careful not to...

So:

• pazila da ne stanu na puža
  literally: were careful that they do not step on the snail
• natural English: were careful not to step on the snail

This is a very common Croatian structure.

Stanu is the 3rd person plural present form of stati.

In this sentence, stati na means to step on.

So:

• da ne stanu na puža = so that they do not step on the snail / not to step on the snail

A useful contrast:

• stati = to step / to stop depending on context
• stajati = to be standing

Here the meaning is clearly step on, because of na puža.

Not always, but very often when the object is something on the ground or something your foot can land on.

So in this sentence:

• stati na puža = to step on a snail

The basic idea is to place your foot onto something. In context, English naturally translates that as step on.

Because stati na takes the accusative case.

The noun is:

• nominative: puž = snail
• accusative: puža

Why does the accusative look different? Because puž is a masculine animate noun. For masculine animate nouns, the accusative singular usually matches the genitive singular.

So:

• vidim puža
• stati na puža

If it were a masculine inanimate noun, the accusative would usually look like the nominative.

Dok here means while or as.

It introduces an action happening at the same time as the main action:

• Djeca su pazila...
• dok su izlazila iz kuće

So the sense is:

• The children were being careful not to step on the snail while/as they were leaving the house.

Because the sentence describes an ongoing background action.

• izlaziti is imperfective
• izlazila suggests were going out / were leaving
• with dok, this is the natural choice for an action in progress

So:

• dok su izlazila iz kuće = while they were leaving the house

If you used a perfective form, the meaning would shift toward a completed action, which would not fit this while it was happening idea as well.

Because the preposition iz means out of or from inside, and it requires the genitive case.

The noun is:

• nominative: kuća = house
• genitive: kuće

So:

• iz kuće = out of the house

Croatian often leaves out subject pronouns when they are already clear from context.

Here, the main subject is Djeca, and the verb forms in the subordinate clauses are plural, so the listener naturally understands that the subject is still the children.

So Croatian does not need to repeat:

• Djeca su pazila da ona ne stanu...
• ...dok su ona izlazila...

That would usually sound unnecessary.

Yes. Croatian word order is more flexible than English word order.

This sentence is neutral and natural:

• Djeca su pazila da ne stanu na puža dok su izlazila iz kuće.

But Croatian can move elements around for emphasis, for example:

• Dok su izlazila iz kuće, djeca su pazila da ne stanu na puža.

One thing to notice is that su is a clitic, so it tends to stay near the beginning of its clause, usually in second position. That is why Djeca su pazila sounds normal, but placing su randomly elsewhere would not.