Až skončí škola, děti položí bundy a batohy ke dveřím a poběží na hřiště.

Here až means when, once, or as soon as in reference to a future event.

So Až skončí škola... means something like:

• When school ends...
• Once school is over...
• As soon as school ends...

A very important point: in Czech, až is commonly used for a specific event that is still in the future. That is why it fits this sentence well.

Because skončit is a perfective verb.

In Czech, perfective verbs often use their present-tense forms to express future meaning. So:

• skončí = it will end / it ends in a future sense
• položí = they will put down
• skončit cannot normally mean an ongoing present action like is ending right now

So Až skončí škola literally uses a present-looking form, but the meaning is future: when school ends.

Yes. Škola is the subject of skončí.

The structure is literally:

• škola skončí = school will end

In English, we also sometimes say school ends, but more often we might say school is over or classes end. In Czech, using škola this way is completely natural.

In this sentence, škola usually means the school day / classes, not the building itself.

Not if you want the same meaning.

Až děti skončí školu usually means something more like:

• When the children finish school
• When they complete their schooling
• When they graduate / finish that school

That is different from when today's school/classes end.

For the meaning in your sentence, Až skončí škola or Až skončí vyučování is more natural.

Položí comes from položit, which is a perfective verb meaning to put down / place as a completed action.

So děti položí bundy a batohy ke dveřím means the children will put down their jackets and backpacks there, as a single completed act.

If you used an imperfective verb instead, the focus would be more on the process or repeated action. Here the sentence is describing a simple sequence of events:

1. school ends
2. they put their things down
3. they run to the playground

So položí is a very natural choice.

They are in the accusative plural, because they are the direct objects of položí.

The children are putting down what?

• bundy
• batohy

So those nouns must be in the accusative.

In this particular sentence, the accusative plural forms happen to look the same as the nominative plural:

• bundy
• batohy

That can make the case less obvious to learners, but syntactically they are accusative objects.

Both k and ke mean to / toward here, and both take the dative case.

The noun dveře is a plural-only noun, and its dative plural form is:

• dveřím

So:

• k/ke dveřím = to the door / by the door

Czech often uses ke instead of k when it sounds easier to pronounce before certain consonant combinations. Ke dveřím is the normal, natural form here.

So the important points are:

• ke is just a phonetic variant of k
• dveřím is dative plural

Because with verbs of placement, Czech often uses k/ke + dative to express putting something up near or toward a person or object.

So položí bundy a batohy ke dveřím means they place them by the door / near the door.

It does not necessarily mean strong motion toward the door in an English dramatic sense. It is just the normal Czech way to say where the items are placed.

Because this sentence expresses motion toward a destination.

With na, Czech distinguishes:

• na + accusative = motion to / onto
• na + locative = location on / at

So:

• na hřiště = to the playground
• na hřišti = at the playground

Since the children are running to the playground, Czech uses na hřiště.

Because Czech normally views a hřiště as an open area or surface-like destination, so it uses na rather than do.

Very roughly:

• na is often used with open areas, events, institutions, and surfaces
• do is often used for going inside an enclosed space

So:

• na hřiště = to the playground / sports field
• do hřiště would sound unnatural in standard Czech

This is something you largely have to learn with each noun and place expression.

Because běžet belongs to a group of motion verbs that often form the future with a special simple form rather than bude + infinitive.

So the normal future is:

• poběžím
• poběžíš
• poběží
• etc.

That is why the sentence has poběží na hřiště = they will run to the playground.

For many learners, this looks like a prefixed perfective verb, but here it functions as the standard future form of běžet.

Not really, at least not in the usual lexical sense.

In many Czech verbs, a prefix changes the meaning or makes the verb perfective. But in forms like poběží, poletí, pojede, půjde, the form is simply the normal future of a motion verb.

So here poběží should just be understood as will run, not as a separate vocabulary item with a strong extra meaning like run a bit.

Because Czech often omits possessive words when the ownership is obvious from context.

Here it is naturally understood that the children will put down their own jackets and backpacks. So Czech does not need to say their explicitly.

If you wanted to make it explicit, you could say:

• děti položí své bundy a batohy...

But in many everyday sentences, leaving out the possessive sounds more natural.

Because Až skončí škola is a subordinate clause at the beginning of the sentence.

Czech separates that clause with a comma:

• Až skončí škola, děti...

After that, the main clause begins:

• děti položí bundy a batohy ke dveřím a poběží na hřiště

There is no comma before the second a, because there it is just linking two coordinated verbs with the same subject:

• položí
• poběží