Mia fratino transloĝiĝos sabate.

Esperanto always stresses the second-to-last syllable.

• Mia → MI-a
• fratino → fra-TI-no
• transloĝiĝos → trans-lo-Ĝi-ĝos
• sabate → sa-BA-te

A useful sound here is ĝ, which is pronounced like the j in judge.

Mia means my.

It is a possessive adjective, so it works a lot like an adjective in Esperanto. That means it can match the noun if needed:

• mia fratino = my sister
• miaj fratinoj = my sisters
• mian fratinon = my sister, as a direct object

In this sentence, the noun is singular and not accusative, so plain mia is correct.

In Esperanto, a possessive like mia usually already makes the noun definite, so la is normally not used.

So:

• mia fratino = my sister

not usually:

• la mia fratino

Using la with a possessive is only for special emphasis or contrast, not for ordinary sentences.

It is built from:

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

So fratino means sister.

This is a very common Esperanto pattern:

• patro = father
• patrino = mother
• kato = tomcat/cat
• katino = female cat

Because fratino is the subject of the sentence, not the direct object.

The sister is the one doing or undergoing the action:

• Mia fratino transloĝiĝos = My sister will move

In Esperanto, -n usually marks:

1. a direct object
2. sometimes direction toward something

Neither of those applies to fratino here.

It breaks down like this:

• trans- = across, from one place to another
• loĝ = live, reside
• -iĝ- = become, undergo a change
• -os = future tense

So transloĝiĝos means something like will undergo a change of residence, which in normal English is simply will move or will move house.

This is a very Esperanto-like way of building meaning from smaller parts.

The suffix -iĝ- often shows that the subject itself undergoes a change or comes into a new state.

So:

• transloĝiĝi = to move house, to relocate

It is the normal intransitive idea: the subject changes where they live.

That is why this sentence is not about moving something else. It is about the sister herself changing residence.

No.

English sometimes makes learners think of move oneself, but Esperanto does not need sin here. The verb transloĝiĝi already has the meaning to move / relocate oneself in an intransitive way.

So this is correct:

• Mia fratino transloĝiĝos.

Not:

• Mia fratino sin transloĝiĝos.

Because Esperanto puts tense directly on the verb with endings.

• -as = present
• -is = past
• -os = future
• -us = conditional
• -u = imperative/jussive

So transloĝiĝos already means will move. You do not need an extra word like English will.

Because sabate is the adverbial form.

• sabato = Saturday
• sabate = on Saturday / on Saturdays

Esperanto often uses the -e ending to express time in an adverb-like way. So sabate means on Saturday very naturally here.

A noun form can also be used for time expressions in some cases, often with -n:

• sabaton = on Saturday

But sabate is very common and straightforward.

Yes, depending on context.

By itself, sabate can mean either:

• on Saturday
• on Saturdays

In this sentence, because it describes a single future event, most people will naturally understand on Saturday.

If you want to make repetition clearer, you can say things like:

• ĉiun sabaton = every Saturday
• ĉiusabate = every Saturday

Yes. Esperanto word order is fairly flexible.

For example, these are both natural:

• Mia fratino transloĝiĝos sabate.
• Sabate mia fratino transloĝiĝos.

The second version emphasizes sabate a bit more.

The original order is neutral and very natural.