Na wystawie dzieci pokazały szesnaście rysunków zrobionych kredą.

Na wystawie means at the exhibition. Here na is the normal Polish preposition for many events, exhibitions, fairs, concerts, and similar public occasions.

Wystawie is the locative singular form of wystawa. After na in a location meaning, Polish uses the locative:

• wystawa → na wystawie
• koncert → na koncercie

So this is not a literal on in the English sense. It is just the Polish pattern.

For this meaning, Polish normally says na wystawie.

• na wystawie = at the exhibition
• w wystawie would usually sound wrong for this meaning

Very broadly, Polish often uses na for events and organized public activities, even where English uses at or sometimes in.

Dzieci is the nominative plural of dziecko.

This noun is irregular:

• singular: dziecko = child
• plural: dzieci = children

Because dzieci is the subject of the sentence, it appears in the nominative.

In the Polish past tense, the verb agrees with the subject in number and in the special plural distinction between masculine personal and non-masculine-personal.

Dzieci takes the non-masculine-personal plural form, so the verb is:

• pokazały

Compare:

• chłopcy pokazali = the boys showed
• dzieci pokazały = the children showed

Even if the group of children includes boys, the noun dzieci still takes pokazały.

This is a question of aspect.

• pokazały is perfective: it presents the action as completed
• pokazywały is imperfective: it focuses on the process, duration, or repetition

So here pokazały means that the children showed the drawings as a completed event. If you said pokazywały, it would suggest something more like were showing, used to show, or showed repeatedly, depending on context.

After numerals 5 and higher, Polish normally uses the genitive plural of the counted noun.

So:

• jeden rysunek
• dwa rysunki
• trzy rysunki
• cztery rysunki
• pięć rysunków
• szesnaście rysunków

That is why you get rysunków, not rysunki.

Because the whole phrase szesnaście rysunków functions as the object.

A useful way to think about it is:

• the verb pokazały takes a direct object
• that object is the whole numeral phrase szesnaście rysunków
• inside that phrase, the noun rysunków appears in the genitive plural because that is what szesnaście requires

So yes, the sentence still has a direct object, even though the counted noun itself is in the genitive form.

Zrobionych is a participle used like an adjective. It comes from zrobić and means made or done.

Here it describes rysunków, so it has to match that noun grammatically. Since rysunków is in the genitive plural, the participle is also in the genitive plural:

• rysunków zrobionych kredą

So the structure is basically:

• drawings made with chalk

Because zrobionych has to agree with rysunków.

The noun rysunków is in the genitive plural, so the modifying participle must also be in the genitive plural:

• rysunków zrobionych

If the noun were in a different form, the participle would change too. Polish modifiers have to agree with the nouns they describe.

Kredą is the instrumental singular of kreda.

Polish often uses the instrumental case to show the tool, instrument, or medium used to do something:

• pisać długopisem = to write with a pen
• malować farbami = to paint with paints
• rysować kredą = to draw with chalk

So zrobionych kredą means the drawings were made using chalk.

Not if you want the same meaning.

• kredą = with chalk, using chalk as a tool or medium
• z kredy = out of chalk, made from chalk as a material

So for drawings, kredą is the natural choice. Z kredy would suggest something physically made from chalk, not drawn with it.

Zrobionych kredą is grammatical and understandable. But narysowanych kredą is more specific and often sounds more natural, because it literally means drawn with chalk.

So:

• rysunki zrobione kredą = drawings made with chalk
• rysunki narysowane kredą = drawings drawn with chalk

The sentence you were given is fine, but narysowanych is a more precise choice.

Yes. Polish word order is quite flexible.

This sentence begins with Na wystawie to set the scene first:

• Na wystawie dzieci pokazały szesnaście rysunków zrobionych kredą.

You could also say:

• Dzieci pokazały na wystawie szesnaście rysunków zrobionych kredą.

Both are correct. The main difference is emphasis:

• starting with Na wystawie highlights the location
• starting with Dzieci highlights the subject first

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

So nouns appear without an article:

• dzieci can mean children or the children
• rysunków can mean drawings or the drawings

The exact meaning is understood from context.