Na ścianie wisi szesnaście rysunków z wakacji.

Because na can mean either:

• location: on
• movement toward a surface: onto

Here the sentence describes where the drawings are, not movement, so Polish uses the locative:

• na ścianie = on the wall

Compare:

• Rysunki są na ścianie. = The drawings are on the wall.
• Wieszam rysunki na ścianę. = I’m hanging the drawings onto the wall.

So:

• na ścianie = location
• na ścianę = direction/movement

Ścianie is the locative singular of ściana.

The dictionary form is:

• ściana = wall

After na meaning on in a location sense, Polish uses the locative:

• na ścianie = on the wall

So this is a normal case change:

• ściana → ścianie

This is a very common Polish pattern with numbers.

With 5 and above, the counted noun usually goes into the genitive plural, and the whole number phrase often takes a singular verb in sentences like this.

So:

• trzy rysunki wiszą = three drawings are hanging
• szesnaście rysunków wisi = sixteen drawings are hanging

To an English speaker, that feels odd, because English always uses a plural verb here. But in Polish, phrases with numbers like pięć, sześć, szesnaście, dwadzieścia often behave differently from ordinary plural nouns.

A useful comparison:

• Na ścianie wiszą trzy rysunki.
• Na ścianie wisi szesnaście rysunków.

Because after szesnaście (like after most numbers 5+), Polish uses the genitive plural of the noun.

The dictionary form is:

• rysunek = drawing

Its genitive plural is:

• rysunków

So:

• jeden rysunek = one drawing
• dwa / trzy / cztery rysunki = two / three / four drawings
• pięć / szesnaście rysunków = five / sixteen drawings

This is one of the basic number patterns in Polish:

• 1 → nominative singular
• 2–4 → nominative plural form
• 5+ → genitive plural

Because z here means from, and z in that meaning takes the genitive.

So:

• z wakacji = from the holidays / from vacation

The noun is:

• wakacje = holidays, vacation

Its genitive form is:

• wakacji

So the phrase means that the drawings are connected with, or come from, the vacation period.

Yes — wakacje is a plural-only noun in Polish.

That means Polish normally talks about vacation/holidays in the plural:

• wakacje były udane = the vacation/holidays were successful

This is different from English, which can use singular vacation.

A related word is:

• urlop = leave, time off work

So depending on context:

• wakacje often refers to school holidays or a vacation period
• urlop often means an adult’s leave from work

Because Polish often prefers a verb that describes an object’s position.

Common verbs like this are:

• wisieć = to hang
• stać = to stand
• leżeć = to lie

So Polish naturally says:

• Na ścianie wisi obraz. = A picture is hanging on the wall.
• Na stole leży książka. = A book is lying on the table.
• Przy oknie stoi lampa. = A lamp is standing by the window.

Using jest is sometimes possible in other contexts, but here wisi is much more natural.

They are related, but they are not the same.

• wisieć = to be hanging
  This describes a state.
• wieszać = to hang, to be hanging up
  This describes an action and is imperfective.
• powiesić = to hang up
  This describes a completed action and is perfective.

Examples:

• Rysunki wiszą / wisi na ścianie. = The drawings are hanging on the wall.
• Wieszam rysunki na ścianie. = I am hanging the drawings on the wall.
• Powiesiłem rysunki na ścianie. = I hung the drawings on the wall.

So in your sentence, wisi is used because it describes the finished result: the drawings are already there, hanging.

Yes. Polish word order is fairly flexible.

The original sentence:

• Na ścianie wisi szesnaście rysunków z wakacji.

A different order could be:

• Szesnaście rysunków z wakacji wisi na ścianie.

Both are correct. The difference is mainly focus or emphasis:

• Na ścianie... puts the location first, like setting the scene.
• Szesnaście rysunków... puts the drawings/number first.

So the original version sounds very natural if you want to start with where something is.

Because they mean different things.

• z wakacji = from the holidays / from vacation
• na wakacjach = on vacation / during the holidays

In your sentence, z wakacji describes the drawings as drawings from that vacation period.

So:

• rysunki z wakacji = drawings from vacation

But:

• na wakacjach would refer to being somewhere during vacation, for example:
  • Byliśmy nad morzem na wakacjach. = We were at the seaside on vacation.

So z wakacji is the correct phrase here.