A giugno la scuola finisce, e mia sorella è molto felice.

In Italian, months are commonly used with a to mean in a certain month: a giugno, a luglio, a settembre, etc.

So:

• a giugno = in June

You may also sometimes see in giugno, but a giugno is the more natural and usual choice in everyday Italian.

Scuola is a noun, and here it means school in a general sense, so Italian normally uses the definite article:

• la scuola = school / the school

Italian uses articles more often than English does. Where English might say school ends, Italian naturally says la scuola finisce.

Finisce is the third person singular present tense of finire:

• finire = to finish, to end
• finisce = it ends / ends

Since the subject is la scuola (a singular noun), the verb is singular too:

• la scuola finisce = school ends

Italian often uses the present tense for things that are scheduled, regular, or understood as part of a calendar or routine.

So A giugno la scuola finisce can mean:

• In June school ends
• School ends in June

This is very natural in Italian, just like English can say School ends in June using the present tense.

With singular family members, Italian usually drops the article before the possessive:

• mia sorella = my sister
• mio fratello = my brother
• mia madre = my mother

So mia sorella is the normal form.

But there are exceptions. The article is often used when:

• the family noun is plural: le mie sorelle
• the noun is modified: la mia sorella maggiore
• certain forms are used, especially affectionate or less basic ones

So in this sentence, mia sorella is exactly what you would expect.

È is the verb essere (to be) in the third person singular:

• è = is

Felice is an adjective meaning happy.

So:

• mia sorella è molto felice = my sister is very happy

Italian uses essere + adjective here, just like English uses to be + adjective.

Some Italian adjectives have the same form for masculine singular and feminine singular.

Felice is one of them:

• lui è felice = he is happy
• lei è felice = she is happy

It does change in the plural:

• felici = happy (plural)

So mia sorella è molto felice is correct even though sorella is feminine.

They are two different words:

• e = and
• è = is

In your sentence:

• ..., e mia sorella... = ..., and my sister...
• mia sorella è molto felice = my sister is very happy

The accent matters a lot. Without it, the meaning changes.

The comma separates the two parts of the sentence:

• A giugno la scuola finisce
• e mia sorella è molto felice

In Italian, a comma before e is possible when the writer wants a slight pause or clearer separation. It is not always required, and you could also see:

• A giugno la scuola finisce e mia sorella è molto felice.

Both are understandable. The version with the comma just gives a bit more pause.

Yes, Italian word order is fairly flexible, although some versions sound more neutral than others.

The given sentence is very natural:

• A giugno la scuola finisce, e mia sorella è molto felice.

You could also say:

• La scuola finisce a giugno, e mia sorella è molto felice.

That puts a little less focus on June and a little more on school ends as the main statement.

So both are correct, but starting with A giugno highlights the time first.

Here molto is functioning as an adverb, meaning very:

• molto felice = very happy

It is modifying the adjective felice.

In other contexts, molto can also be an adjective meaning much / a lot of, but not here. In this sentence, it simply intensifies felice.