Elokuu on se kuukausi, jolloin uusi lukuvuosi alkaa.

Se here means something like the / that. The phrase se kuukausi, jolloin... means the month when....

So:

• Elokuu on kuukausi = August is a month
• Elokuu on se kuukausi, jolloin... = August is the month when...

In this sentence, se helps make the noun phrase more specific. It points forward to the relative clause jolloin uusi lukuvuosi alkaa and gives the sense of the particular month in which....

In English, this is very natural with the. Finnish does not have articles, so words like se often help express that kind of definiteness.

Jolloin means when, especially in a relative-clause sense: the time/month/day when...

In this sentence:

• se kuukausi, jolloin uusi lukuvuosi alkaa
  = the month when the new school year begins

It is built from the relative/interrogative stem joka and a case form related to time. You do not need to analyze it every time, but it is useful to recognize that jolloin is commonly used after time words such as:

• päivä, jolloin... = the day when...
• vuosi, jolloin... = the year when...
• aika, jolloin... = the time when...

Sometimes yes, but jolloin is better here.

Compare:

• Elokuu on se kuukausi, jolloin uusi lukuvuosi alkaa.
• Elokuu on se kuukausi, kun uusi lukuvuosi alkaa.

The version with jolloin sounds more standard and more clearly connected to kuukausi. It is the usual choice in careful written Finnish when you mean the month when...

Kun also means when, but it is more general and often used in everyday speech for many kinds of time clauses. Learners will often hear it, but in this sentence jolloin is the most natural textbook-style form.

Because it is the predicate noun after on.

The sentence structure is:

• Elokuu = subject
• on = is
• se kuukausi = predicate noun phrase

In Finnish, predicate nouns after olla are often in the nominative when they identify what something is.

So:

• Elokuu on kuukausi = August is a month
• Elokuu on se kuukausi... = August is the month...

That is why kuukausi is in nominative singular.

Because it agrees with lukuvuosi, which is nominative singular here.

• uusi = new
• lukuvuosi = school year / academic year

Since lukuvuosi is nominative singular, the adjective describing it is also nominative singular:

• uusi lukuvuosi

This is normal Finnish adjective agreement.

Lukuvuosi means school year or academic year, depending on context.

It is a compound word:

• luku can relate to study/reading
• vuosi = year

In practice, lukuvuosi refers to the yearly period of schooling or study, not the calendar year.

So in this sentence, uusi lukuvuosi alkaa means the new school year begins.

Because the subject of that clause is singular:

• uusi lukuvuosi = the new school year

That is one thing, so the verb is third person singular:

• alkaa = begins / starts

If the subject were plural, the verb would also be plural:

• uudet lukuvuodet alkavat = the new school years begin

So here:

• uusi lukuvuosi alkaa = singular subject + singular verb

It breaks down like this:

• Elokuu = August
• on = is
• se kuukausi = the month
• jolloin = when
• uusi lukuvuosi = the new school year
• alkaa = begins

So the structure is:

August is the month when the new school year begins.

A useful way to see it is:

1. Main clause: Elokuu on se kuukausi
2. Relative clause: jolloin uusi lukuvuosi alkaa

The relative clause describes kuukausi.

No. In standard Finnish, names of months are normally written with a lowercase letter, unless they begin a sentence.

So:

• elokuu = normal spelling in the middle of a sentence
• Elokuu = capitalized here because it is the first word of the sentence

This is different from English, where August is always capitalized.

Yes. Finnish has no true articles like English a/an and the.

Instead, Finnish expresses those ideas in other ways, depending on context:

• sometimes with no extra word at all
• sometimes with word order
• sometimes with pronouns like se
• sometimes the meaning is just understood from context

In this sentence, se kuukausi helps express the definite idea the month. But in many other sentences, Finnish would simply use the noun without any article-like word, and the context would tell you whether it means a month or the month.