La urbo ŝanĝiĝis dum la jarcento.

It is made of three parts:

• ŝanĝ- = the idea of changing
• -iĝ- = becoming, getting into a new state, undergoing a change
• -is = past tense

So ŝanĝiĝis means that something underwent change or changed in the past.

Because Esperanto makes an important distinction here:

• ŝanĝi / ŝanĝis is usually transitive: someone or something changes something else
• ŝanĝiĝi / ŝanĝiĝis is intransitive: the subject itself changes

So:

• La urbo ŝanĝiĝis = the city changed
• La urbo ŝanĝis la planon = the city changed the plan

In this sentence, the city is the thing that underwent the change, so ŝanĝiĝis is the natural form.

No.

In ŝanĝiĝis, the word is divided as:

• ŝanĝ-
• -iĝ-
• -is

So the letters ĝis here are just part of the verb’s internal structure. They are not the separate preposition/adverb ĝis meaning until.

This is a very common thing for learners to notice, because it looks familiar, but it is only a coincidence of spelling.

Because urbo is the subject of the sentence.

In Esperanto, the -n ending marks the direct object. But here the city is not receiving an action from something else; it is the thing that changed.

So:

• La urbo ŝanĝiĝis = correct
• La urbon ŝanĝiĝis = wrong

Because dum is a preposition, and prepositions normally take the basic noun form, not the accusative.

So:

• dum la jarcento = during the century

The preposition already shows the role of the phrase, so no extra -n is needed.

Here dum means during or throughout a period of time.

So dum la jarcento means something like:

• during the century
• over the course of the century
• throughout the century

A useful point: with a noun phrase, dum usually means during a time span.
With a full clause, it can mean while.

For example:

• dum la nokto = during the night
• dum mi legis = while I was reading

Because la marks a specific thing, just like the in English.

So la urbo means the city, not just a city.

Without la, urbo would sound more general or indefinite.

Because it usually refers to a specific century or to the century being discussed.

So dum la jarcento suggests:

• during that particular century
• over the course of the century in question

If you removed la, the phrase would usually feel less specific, and in many contexts it could sound more like for a century or for one century, depending on context.

It is a compound word:

• jar- = year
• cent- = hundred
• -o = noun ending

So jarcento literally means hundred-year, which is the Esperanto word for century.

This kind of compounding is very common in Esperanto.

Yes. Esperanto word order is fairly flexible.

The original sentence is neutral:

• La urbo ŝanĝiĝis dum la jarcento.

But you could also say:

• Dum la jarcento la urbo ŝanĝiĝis.

That version puts more attention on the time phrase.

Because Esperanto uses endings and prepositions clearly, moving parts around is often possible without changing the basic meaning.

Yes, but it does not mean exactly the same thing.

• La urbo ŝanĝiĝis = the city changed, the city underwent change
• La urbo estis ŝanĝita = the city was changed

The passive form estis ŝanĝita suggests an outside force more strongly.
The form ŝanĝiĝis is often more natural when you simply want to say that the city became different over time, without focusing on who caused it.