Sabate ni vespermanĝas je la sesa, sed dimanĉe ni vespermanĝas je la naŭa.

Because they are being used as adverbs meaning on Saturday and on Sunday.

The basic noun forms are sabato and dimanĉo. Esperanto often turns time words into adverbs with -e:

• sabato = Saturday
• sabate = on Saturday
• dimanĉo = Sunday
• dimanĉe = on Sunday

This is a very common pattern for days and other time expressions.

It depends on context, but in this sentence it most naturally sounds habitual: on Saturdays ... but on Sundays ...

That is because:

• the verb is in the present tense
• the sentence contrasts Saturday and Sunday as a routine
• there is no extra word pointing to one specific upcoming Saturday

So a learner should probably understand this as a general habit unless the surrounding context says otherwise.

Je is the usual preposition for clock times in Esperanto.

So:

• je la sesa = at six o’clock
• je la naŭa = at nine o’clock

Esperanto uses je in situations where English might use at, especially with times of day.

Because Esperanto normally uses ordinal numbers for clock time:

• la sesa = the sixth
• la naŭa = the ninth

The full idea is really:

• je la sesa horo
• je la naŭa horo

That literally means at the sixth hour and at the ninth hour. In normal speech, horo is usually left out because it is understood.

Because the expression is short for la sesa horo / la naŭa horo.

Since it refers to a specific numbered hour, Esperanto normally uses the definite article:

• je la sesa
• je la naŭa

So the article is part of the normal clock-time expression.

Because the preposition je is already doing the job.

In Esperanto, time expressions can sometimes use the accusative without a preposition, but here the phrase already starts with je, so you do not add -n:

• correct: je la sesa
• not here: je la sesan

The -n ending is not used after je in this kind of ordinary time expression.

It is a compound verb, and Esperanto makes these very freely.

It is built from:

• vesper- = evening
• manĝ- = eat
• -as = present tense

So vespermanĝas means eat the evening meal, that is, have dinner / supper.

Related words include:

• matenmanĝi = eat breakfast
• tagmanĝi = eat lunch / the midday meal
• vespermanĝi = eat dinner / supper

Using one compound word like this is very normal Esperanto.

Because Esperanto uses the present tense for habits, routines, and general facts, just as English does.

So ni vespermanĝas here means something like a regular practice, not necessarily something happening right this second.

This is the normal tense for statements about schedules and habits.

Because the sentence has two full clauses:

• Sabate ni vespermanĝas je la sesa
• sed dimanĉe ni vespermanĝas je la naŭa

Repeating the subject and verb makes the contrast very clear and balanced.

You can sometimes omit repeated material in Esperanto if the meaning is obvious, but the full version is completely natural and often better for clarity.

Because in Esperanto, days of the week are normally not capitalized unless they begin a sentence.

So:

• sabato
• dimanĉo

This is similar to many European languages, but different from English.

Yes, often you can.

Esperanto commonly uses either:

• the adverb form: sabate, dimanĉe
• the accusative of time: sabaton, dimanĉon

Both can mean on Saturday / on Sunday.

Very roughly:

• sabate feels more adverb-like and is very common in general statements
• sabaton uses the time accusative, which is also standard

In a sentence like this, sabate and dimanĉe are especially natural.

A few useful points:

• ĉ sounds like ch in church
• stress in Esperanto normally falls on the second-to-last syllable

So approximately:

• sabate → sa-BA-te
• dimanĉe → di-MAN-che
• vespermanĝas → ves-per-MAN-jas
• sesa → SE-sa
• naŭa → NAŭ-a

Also, ŭ is a very short w-like sound, so naŭa sounds roughly like NOW-ah, but with the stress on the first part.