Ĉiu amiko ricevas po unu tranĉtabulon kaj antaŭtukon.

Because ĉiu means each, and Esperanto normally uses a singular noun after it.

• ĉiu amiko = each friend
• ĉiuj amikoj = all the friends

Both can refer to the same group of people, but the viewpoint is different. Ĉiu amiko looks at them one by one.

Po shows distribution: apiece, each, per person.

So po unu means one each or one apiece.

In this sentence, po unu tells you that the quantity is distributed to each friend individually. It is not one cutting board and one apron for the whole group; it is one for each friend.

Good question. The sentence would still be understandable without po:

Ĉiu amiko ricevas unu tranĉtabulon kaj antaŭtukon.

But po makes the distributive idea more explicit. It emphasizes that the amount is given separately to each person: one each.

So here po is not strictly necessary for basic understanding, but it is very natural if the speaker wants to stress the per-person distribution.

Because they are direct objects of ricevas.

The sentence is about what each friend receives, and the things being received are:

• tranĉtabulon
• antaŭtukon

In Esperanto, direct objects take the accusative ending -n.

Also, when two nouns are joined by kaj, each one keeps its own ending if both have the same grammatical role. That is why both words end in -n.

Yes. In this sentence, the natural reading is:

• one cutting board
• and one apron

for each friend.

Esperanto often lets one quantity word cover a coordinated pair like this when the same number applies to both items.

If someone wants to be extra explicit, they can repeat unu:

Ĉiu amiko ricevas po unu tranĉtabulon kaj unu antaŭtukon.

But the original sentence is perfectly normal.

Esperanto has la for the, but it does not have an indefinite article like English a/an.

So Esperanto often uses a bare noun where English would use a or an.

Here:

• amiko = friend or a friend, depending on context
• unu explicitly gives the idea of one / a single
• ĉiu already works as a determiner meaning each

So no article is needed.

It is a compound word:

• tranĉ- = cut
• tabulo = board

So tranĉtabulo is literally a cutting-board, a board for cutting on.

Then -n is added because it is a direct object:

• tranĉtabulo = cutting board
• tranĉtabulon = cutting board as a direct object

This is very typical Esperanto word-building.

It is also a compound:

• antaŭ = in front of, before
• tuko = cloth

So antaŭtuko is literally a front-cloth, which is the Esperanto word for apron.

Again, the final -n is the accusative ending:

• antaŭtuko = apron
• antaŭtukon = apron as a direct object

A few useful points:

• ĉ sounds like ch in church
• ŭ appears in diphthongs like aŭ, which sounds roughly like ow in cow
• stress in Esperanto falls on the second-to-last syllable

So:

• ĉiu is roughly CHEE-oo
• tranĉtabulon is stressed on BU: tranĉ-ta-BU-lon
• antaŭtukon is stressed on TU: an-taŭ-TU-kon

The spelling is very regular, so once you know the letter sounds, pronunciation becomes much easier.