Mi matenmanĝas je la sepa, sed mia fratino matenmanĝas je la oka.

It is a compound verb:

• maten- = morning
• manĝ- = eat
• -as = present tense

So matenmanĝas literally means something like morning-eats, and idiomatically it means eats breakfast or has breakfast.

A related noun is matenmanĝo = breakfast.

In Esperanto, the present tense often describes a habitual action, just like in English:

• Mi matenmanĝas je la sepa = I eat breakfast at seven / I have breakfast at seven

So this sentence is most naturally understood as a routine, not necessarily something happening right this second.

Repeating the verb makes the sentence very clear and balanced:

• Mi matenmanĝas je la sepa, sed mia fratino matenmanĝas je la oka.

You can often omit the second verb if it is obvious:

• Mi matenmanĝas je la sepa, sed mia fratino je la oka.

That is still understandable. The full version is just a bit more explicit.

Je is a general-purpose preposition. It is often used for clock times:

• je la sepa = at seven
• je la oka = at eight

For telling time, je is the normal and easy choice. It does not have one single concrete meaning like in or on; it often just marks a relationship that Esperanto does not want to express more specifically.

In this style of time expression, Esperanto often uses ordinal numbers:

• sepa = seventh
• oka = eighth

So je la sepa literally means at the seventh hour, and je la oka means at the eighth hour.

The noun horo is understood but left out.

Because the full idea is:

• je la sepa horo
• je la oka horo

Since horo is omitted, la stays. This is the standard way to express this kind of clock time.

The ending -a makes them adjectives, and ordinal numbers in Esperanto are adjectives:

• sep = seven
• sepa = seventh
• ok = eight
• oka = eighth

In the time expression, they are really describing the understood noun horo:

• la sepa (horo)
• la oka (horo)

Because they are not direct objects here.

They are part of a prepositional phrase introduced by je:

• je la sepa
• je la oka

After a preposition like je, you normally do not add the accusative -n unless there is some special reason, and there is no such reason here.

• mia = my
• fratino = sister

The word fratino is built from:

• frat- = sibling/brother root
• -in- = female
• -o = noun

So fratino is the feminine form meaning sister.

Also, mia does not change here. Possessive words like mia, via, lia, and so on work like adjectives, but in this sentence mia stays simple because there is no plural or accusative marking needed.

Sed means but. It shows a contrast:

• I eat breakfast at seven,
• but my sister eats breakfast at eight.

If you used kaj, that would just join the two facts without highlighting the contrast.

Not by itself. It simply means at seven o’clock.

In this sentence, the context makes it clear that it is morning, because the verb is matenmanĝas = has breakfast. So most readers will understand it as 7 a.m.

If you needed to be extra clear, you could add something like matene = in the morning.

No. It is a very common and natural way, but not the only one.

You could also say:

• manĝi matenmanĝon = eat breakfast

But matenmanĝi is neat and idiomatic, so it is a very good form to learn.

The given word order is the most straightforward one:

• Mi matenmanĝas je la sepa
• sed mia fratino matenmanĝas je la oka

Esperanto word order is fairly flexible, but this normal order is best for learners because it is clear and neutral:

• subject
• verb
• time expression

So yes, other orders may be possible in context, but this one is the standard, unmarked way to say it.