Ekde septembro mia amikino iros al la universitato en alia urbo, sed ŝi promesis skribi al mi ĉiun semajnon.

In Esperanto, names of months and weekdays are normally written with lowercase letters: januaro, februaro, septembro, and so on.

So septembro is lowercase unless it begins a sentence or is part of a title.

Ekde means starting from or from ... onward.

• de by itself often just means from
• ekde makes the starting point especially clear

So Ekde septembro means starting in September / from September onward.

Iros is the future tense of iri (to go).

Esperanto verbs are very regular:

• iri = to go
• iras = go / is going
• iris = went
• iros = will go
• irus = would go

The ending -os always marks the future. It does not change for different persons:

• mi iros
• ŝi iros
• ili iros

all use the same -os ending.

The base word amiko means friend. The suffix -in- marks female sex, so:

• amiko = friend / male friend, depending on context
• amikino = female friend

Since the sentence refers to ŝi (she), amikino fits naturally here.

Al shows movement toward a destination, so with iri (to go) it is very common:

• iri al la domo = go to the house
• iri al la universitato = go to the university

The article la suggests a specific university that is understood from context.

Also, al la universitato means to the university as a destination. If you wanted to stress movement into the university building, Esperanto could also use en with the accusative in some contexts, but al is the normal choice for simply going there.

Because en alia urbo describes where the university is located, not the destination of iros directly.

• en alia urbo = in another city

So the idea is: she will go to a university that is in another city.

If you wanted to say she will go to another city, then you would say:

• ŝi iros al alia urbo

So:

• al = toward a destination
• en = in / inside a location

Because alia belongs to the phrase en alia urbo, and that phrase is just a location.

There is no accusative -n here because nothing in that phrase is a direct object, and en already marks the relationship.

Compare:

• en alia urbo = in another city
• al alian urbon = to another city

In the second example, alian urbon has -n because it shows motion toward a place.

After promesi (to promise), Esperanto often uses the infinitive when the subject is the same:

• ŝi promesis skribi = she promised to write

This works just like English promised to write.

You can also use a full clause with ke:

• ŝi promesis, ke ŝi skribos al mi

That means essentially the same thing, but promesis skribi is shorter and very natural.

Because skribi al iu means to write to someone.

With skribi, the thing being written is the direct object, while the person receiving it usually comes with al:

• skribi leteron = write a letter
• skribi al mi = write to me
• skribi leteron al mi = write a letter to me

So mi becomes al mi, not a direct object.

This is the accusative of time.

Esperanto often uses -n for time expressions without a preposition:

• ĉiun tagon = every day
• ĉiun semajnon = every week
• la tutan jaron = the whole year

So in ĉiun semajnon, the -n marks a time expression meaning every week.

Both words show the accusative:

• ĉiun
• semajnon

Esperanto word order is fairly flexible, because endings do a lot of the grammatical work. The sentence here uses a very normal, neutral order.

For example, you could move some parts for emphasis:

• Mia amikino ekde septembro iros al la universitato en alia urbo...
• Ekde septembro iros mia amikino al la universitato...

These are possible, but the original version sounds straightforward and natural.

So the answer is:

• No, the word order is not completely fixed
• but the given order is the most neutral and easiest for learners to follow