Kelkaj studentoj atendas ĉe la biblioteko post la leciono.

Because -o marks a noun, and -j marks the plural in Esperanto.

So:

• studento = student
• studentoj = students

Here the sentence is talking about more than one student, so studentoj is plural.

Because kelkaj is describing the plural noun studentoj, so it also takes the plural ending -j.

• kelka studento = some student / a certain student
• kelkaj studentoj = some students

Words that act like adjectives in Esperanto usually agree with the noun in number, and sometimes in case too.

Because this phrase is the subject of the sentence, not the direct object.

In Esperanto, the -n ending marks the direct object. Here, some students are the ones doing the waiting, so they are the subject:

• Kelkaj studentoj atendas... = Some students are waiting...

If the students were the object, then you would use -n:

• Mi vidas kelkajn studentojn. = I see some students.

In Esperanto, -as is the present tense verb ending.

So:

• atendi = to wait
• atendas = wait / is waiting / are waiting

Esperanto verbs do not change depending on the subject, so:

• mi atendas = I wait
• li atendas = he waits
• ili atendas = they wait

The ending stays -as for all persons in the present tense.

Because Esperanto usually does not need an extra helping verb like English does in the present progressive.

English says:

• Some students are waiting

Esperanto simply uses the present tense verb:

• Kelkaj studentoj atendas

This can mean wait or are waiting, depending on context.

Ĉe usually means at, by, with, or in the vicinity of.

So:

• ĉe la biblioteko = at the library / by the library

This does not necessarily mean they are inside the library. It just places them at that location.

If you wanted to say they are physically inside the library, en la biblioteko would more strongly mean in the library.

So the difference is roughly:

• ĉe la biblioteko = at the library
• en la biblioteko = in the library

La is the definite article, meaning the.

So:

• biblioteko = library
• la biblioteko = the library

Esperanto has only one article, la, and it never changes form.

The sentence uses la biblioteko because it refers to a specific library, or one that is understood from the context.

Because both are part of prepositional phrases:

• ĉe la biblioteko
• post la leciono

Normally, nouns after prepositions do not take the accusative -n.

So here:

• ĉe la biblioteko = at the library
• post la leciono = after the lesson

There is no direct object here, so no -n is needed.

It means after the lesson.

Breakdown:

• post = after
• la = the
• leciono = lesson

So the whole phrase tells us when the students are waiting.

Using la suggests a specific lesson that both speaker and listener can identify from context.

So:

• post leciono would sound more general or less natural in many contexts
• post la leciono = after the lesson, meaning a particular lesson

Esperanto often uses la when the thing being referred to is understood from the situation.

Yes, Esperanto word order is fairly flexible.

The neutral order here is:

• Kelkaj studentoj atendas ĉe la biblioteko post la leciono.

But other orders are possible for emphasis, such as:

• Post la leciono, kelkaj studentoj atendas ĉe la biblioteko.
• Ĉe la biblioteko atendas kelkaj studentoj post la leciono.

The basic meaning stays clear because Esperanto uses endings like -j and -n rather than relying as heavily on word order as English does.

Yes, in this sentence kelkaj means some in the sense of a number of, but not all.

So:

• kelkaj studentoj = some students

It usually suggests an unspecified smaller group.

Compare:

• kelkaj studentoj = some students
• ĉiuj studentoj = all students
• multaj studentoj = many students

A rough pronunciation guide is:

KEL-kai stoo-DEN-toy ah-TEN-dahs cheh lah bib-lee-o-TEH-koh post lah leh-tsee-OH-no

A few useful points:

• j sounds like English y
• ĉ sounds like ch
• every vowel is pronounced clearly
• stress is always on the second-to-last syllable

So:

• kelkaj → KEL-kai
• studentoj → stoo-DEN-toy
• biblioteko → bib-lee-o-TEH-ko
• leciono → leh-tsee-O-no