Post la ekzameno la studentoj ridetas unu al la alia.

Because post means after, and post la ekzameno is a time expression meaning after the exam.

Esperanto often puts time expressions near the beginning of the sentence, but it does not have to. You could also say:

La studentoj ridetas unu al la alia post la ekzameno.

Both are correct. Starting with Post la ekzameno just gives the time setting first.

Because post is a preposition, and after a preposition Esperanto normally uses the basic noun form, not the accusative.

So:

• post la ekzameno = after the exam
• not post la ekzamenon

The -n ending is mainly used for a direct object or for direction/motion in certain cases. Here la ekzameno is simply the object of the preposition post.

Because these are two separate noun phrases, and each one can take its own definite article.

• la ekzameno = the exam
• la studentoj = the students

This is normal in Esperanto, just as in English you would say After the exam, the students...

The ending -j marks the plural in Esperanto.

So:

• studento = student
• studentoj = students

This is one of the most basic Esperanto endings:

• -o = noun
• -j = plural

So studentoj literally means student + plural.

Because ridetas uses the suffix -et-, which adds the idea of smallness, slightness, or gentleness.

• ridi = to laugh
• rideti = to smile, or to laugh a little / softly

So ridetas is the present tense of rideti:

• ridet-as = are smiling

This is a very common way Esperanto builds related meanings from one root.

It has three parts:

• rid- = the root related to laughing
• -et- = a suffix meaning a little, slight, or gentle
• -as = present tense verb ending

So:

rid-et-as = smiles / are smiling

Esperanto words are often built very regularly like this, which is one of the language’s main features.

Because unu al la alia is a standard reciprocal expression in Esperanto.

Literally, it means something like one to the other. In natural English, though, it corresponds to each other.

In this sentence:

la studentoj ridetas unu al la alia

the idea is that the students are smiling at each other.

This structure is very common:

• ili helpas unu la alian = they help each other
• ili parolas unu al la alia = they speak to each other

Because al means to, and with rideti it expresses the direction of the smile: to/at one another.

So:

• rideti al iu = to smile at someone

That is why the sentence says:

ridetas unu al la alia

If the verb were a different one, the reciprocal pattern might look different. For example:

• ili vidas unu la alian = they see each other
• ili skribas unu al la alia = they write to each other

The preposition depends on how the verb works.

Because in the expression unu al la alia, Esperanto treats it as a reciprocal pattern meaning one to the other, not as a normal plural adjective phrase.

So even though several students are involved, the expression stays in this standard form:

unu al la alia

It is best learned as a set phrase meaning each other or one another in contexts with al.

No, not with the same meaning.

sin is a reflexive pronoun, used when the subject acts on itself/himself/herself/themselves. It does not mean each other.

For example:

• Li lavas sin. = He washes himself.
• Ili lavas sin. = They wash themselves.
  This does not specifically mean they wash each other.

To express each other, Esperanto normally uses unu ... la alia(n) or a similar reciprocal pattern.

So here unu al la alia is the correct choice.

No, Esperanto word order is fairly flexible, although some orders sound more natural than others.

These are all possible:

• Post la ekzameno la studentoj ridetas unu al la alia.
• La studentoj ridetas unu al la alia post la ekzameno.

The first version is very natural because it puts the time phrase first. Esperanto uses endings, especially -j and -n, to make relationships clear, so word order is less rigid than in English.

A comma is optional here and often omitted in simple sentences.

So both of these are acceptable:

• Post la ekzameno la studentoj ridetas unu al la alia.
• Post la ekzameno, la studentoj ridetas unu al la alia.

The version without the comma is very common in Esperanto when the opening phrase is short and clear.