Treba im objasniti da na toboganu čekaju red, a ne da idu svi odjednom.

Here treba is being used impersonally. In this kind of sentence, it means something like it is necessary, one should, or someone needs to.

So Treba im objasniti... literally works like It is necessary to explain to them...

Croatian often leaves the person responsible unstated in this structure. English sometimes does the same with it is necessary to..., but Croatian uses it very naturally.

Im is the dative plural clitic form meaning to them.

The verb objasniti takes:

• the thing being explained
• and the person it is explained to

So:

• objasniti nešto nekome = to explain something to someone

Here, im is the nekome part:

• Treba im objasniti... = It is necessary to explain to them...

Because im is a clitic, and Croatian clitics usually go in the second position of the clause.

So even though English would often put to them later, Croatian prefers:

• Treba im objasniti...

This is normal clitic placement, not emphasis.

After impersonal treba, Croatian normally uses an infinitive:

• treba objasniti
• treba čekati
• treba ići

So Treba im objasniti means It is necessary to explain to them.

This is a very common pattern:

• Treba raditi.
• Treba učiti.
• Treba im reći.

This is about aspect.

• objasniti = perfective
• objašnjavati = imperfective

Here objasniti fits because the idea is a complete act of explaining: they need to be told/explained this point.

If you used objašnjavati, it would sound more like:

• explaining repeatedly
• explaining over a period of time
• being in the process of explaining

So objasniti is the natural choice for give them the explanation / make it clear to them.

The first da introduces the content clause after objasniti. It is similar to English that.

So the structure is:

• objasniti nekome da... = to explain to someone that...

In this sentence, the thing that needs to be explained is:

• da na toboganu čekaju red

So:

• Treba im objasniti da... = They need to be told/explained that...

Because na toboganu is locative, and it expresses location:

• na toboganu = on/at the slide

By contrast:

• na tobogan would be accusative, usually meaning motion onto the slide

Compare:

• Djeca su na toboganu. = The children are on the slide.
• Djeca idu na tobogan. = The children are going onto/toward the slide.

Here the sentence is about behavior at the slide, so na toboganu is the right form.

No. čekati red is an idiomatic expression meaning to wait one’s turn.

So here it means they should take turns instead of all going at once.

A few related expressions:

• čekati red = wait one’s turn
• čekati svoj red = wait one’s turn, more explicit
• čekati u redu = wait in a line/queue

That last one is slightly different. čekati u redu focuses more on physically standing in a queue, while čekati red focuses on the idea of turn-taking.

Croatian often leaves svoj unstated when the meaning is obvious.

So:

• čekaju red and
• čekaju svoj red

can both mean they wait their turn

Adding svoj makes it more explicit, but it is not necessary here. The shorter form is very natural.

This is a contrast structure.

• a = and/but/whereas
• ne da here introduces the opposite, unwanted action

So:

• da čekaju red, a ne da idu svi odjednom

means something like:

• that they should wait their turn, and not all go at once
• that they should wait their turn rather than all go at once

It sets up:

• the correct behavior vs.
• the incorrect behavior

Croatian word order is flexible. Both are possible, but the order changes the emphasis a little.

• svi idu odjednom = more neutral
• idu svi odjednom = gives a bit more focus to svi, as in everyone goes at once

Also, Croatian often omits subject pronouns, because the verb ending already shows the subject:

• idu = they go

So svi is not there because Croatian needs a subject pronoun; it is there for emphasis on all of them.

Here odjednom means all at once or at the same time.

So:

• idu svi odjednom = they all go at once

Be aware that odjednom can also mean suddenly in other contexts, but in this sentence it clearly means simultaneously.

Yes, it is natural. A native speaker might also say similar versions, such as:

• Treba im objasniti da na toboganu moraju čekati red.
• Treba im reći da na toboganu čekaju svoj red.
• Treba im objasniti da ne mogu svi ići odjednom.

But the original sentence is perfectly normal and idiomatic. It sounds like something an adult would say about teaching children the rules.