Em setembro, as aulas começam, e eu levo o estojo e o manual na mochila.

Because with months, Portuguese normally uses em:

• em setembro = in September
• em janeiro = in January

You usually do not use the article with months in this kind of expression, so no setembro would sound wrong here.

A useful pattern is:

• em + month → in + month
• em setembro
• em outubro
• em dezembro

Portuguese often uses the definite article more than English does.

So:

• as aulas começam
  literally: the classes begin natural meaning: classes start

In English, we often leave out the in general statements, but Portuguese frequently keeps it.

Here, as aulas refers to classes/school lessons in a general, understood sense: the school term is starting.

Aulas literally means classes or lessons.

Depending on context, as aulas começam can mean:

• classes begin
• lessons start
• school starts / school begins

It does not literally mean the school building itself. It refers to teaching sessions or the start of the school period.

Because the subject is as aulas, which is plural.

• a aula começa = the class starts
• as aulas começam = the classes start

So the verb must agree with the subject:

• singular: começa
• plural: começam

This is a very important feature of Portuguese grammar: verbs change depending on the subject.

Yes, it could just be levo.

Portuguese often drops subject pronouns because the verb ending already shows who the subject is.

• eu levo = I take / I carry
• levo = also I take / I carry

Both are correct. Including eu can add:

• emphasis
• clarity
• contrast

For example:

• Eu levo o estojo, mas ele leva os cadernos.
  I take the pencil case, but he takes the notebooks.

So in your sentence, eu is not required, but it is perfectly natural.

Here levo comes from levar, which often means:

• to take
• to carry

In this sentence, eu levo o estojo e o manual na mochila means something like:

• I take the pencil case and the textbook in my backpack
• I carry the pencil case and the textbook in my backpack

A helpful contrast is:

• levar = to take something from here to there
• trazer = to bring something toward here

English uses take and bring differently depending on perspective, so this can take some practice.

In European Portuguese school vocabulary:

• o estojo usually means the pencil case
• o manual usually means the school textbook

So this sentence is talking about common school items.

A learner might expect manual to mean manual in English, and it can in some contexts, but in school-related Portuguese, manual very often means textbook.

Portuguese often repeats the article before each noun:

• o estojo e o manual

This is very natural and standard.

You may sometimes see article omission in other contexts, but here repeating o clearly marks both nouns as definite and sounds completely normal.

So:

• o estojo e o manual = the pencil case and the textbook

It is the safest pattern for learners to use.

Na is a contraction of:

• em + a = na

So:

• na mochila = in the backpack

Portuguese very often uses an article with nouns like this, where English might prefer a possessive:

• na mochila
  literally: in the backpack natural English meaning here: in my backpack

The context makes it clear whose backpack it is, so Portuguese does not always need minha.

Compare:

• na mochila = in the backpack / in my backpack
• na minha mochila = in my backpack

Both can work, but the version in your sentence is very natural.

The comma after setembro is natural because Em setembro is an introductory time expression:

• Em setembro, ... = In September, ...

The comma before e is a style/pacing choice. Portuguese sometimes uses a comma before e when the sentence has two full clauses or when the writer wants a slight pause:

• as aulas começam
• eu levo o estojo e o manual na mochila

In very simple writing, some people might omit that comma before e, but the sentence as written is acceptable.

Some articles are hard to remove in standard Portuguese without changing the feel of the sentence.

Natural version:

• Em setembro, as aulas começam, e eu levo o estojo e o manual na mochila.

If you remove too many articles, it starts sounding unnatural or incomplete.

For example:

• Em setembro, aulas começam... → not natural here
• ...levo estojo e manual... → also not natural in this context

For English speakers, one key adjustment is that Portuguese often likes articles where English does not.

A close, literal translation would be:

• In September, the classes start, and I take the pencil case and the textbook in the backpack.

But more natural English would usually be:

• In September, classes start, and I take my pencil case and textbook in my backpack.
• In September, school starts, and I carry my pencil case and textbook in my backpack.

This shows an important point: Portuguese and English do not always match word-for-word, especially with:

• articles
• possessives
• school vocabulary

Começam is the they form of começar.

Two spelling points matter here:

• ç gives an s sound before a, o, or u
• ã shows a nasal sound

So começam is roughly pronounced like:

• koo-MEH-sãw

That is only an approximation for an English speaker, but it helps.

Without the cedilla, c before a would sound like a hard k sound, so ç is needed to keep the s sound:

• começa → ko-MEH-sa
• começam → plural form, with nasal ending

This is a very common pattern in Portuguese verb spelling.