Minha irmã fechou a cortina porque o vento na varanda estava muito forte.

Minha means my. It changes form to agree with the noun being possessed, not with the owner.

Here, irmã is a feminine singular noun, so Portuguese uses minha:

minha irmã = my sister

Compare: meu irmão = my brother
minha irmã = my sister

So meu goes with masculine singular nouns, and minha goes with feminine singular nouns.

Portuguese often leaves out subject pronouns when the verb ending already makes the subject clear.

In fechou, the verb form shows he/she/it closed, so ela is not necessary.

So: Minha irmã fechou a cortina
is perfectly natural without saying
Minha irmã ela fechou a cortina

You can include ela in some contexts for emphasis or contrast, but normally it is omitted.

Fechou is the preterite form of fechar for ele/ela/você.

It is used for a completed action in the past. The curtain was closed as a finished event.

So fechou tells you that the action happened and was completed: fechar = to close
fechou = closed

That fits well here because closing the curtain is a single completed action.

Portuguese uses definite articles very often, more often than English does.

Here, a cortina means the curtain. It sounds natural because the speaker has a specific curtain in mind.

Also, cortina is a feminine singular noun, so the article is a: a cortina

If the noun were masculine, it would use o: o livro

Here porque means because, so it is written as one word.

This is the normal form for giving a reason: Ela saiu porque estava cansada.

Learners often confuse these forms:

porque = because
por que = why / for what reason
por quê = why? (usually at the end of a question)
porquê = the reason / the why

In your sentence, it introduces the cause, so porque is correct.

Na is a contraction of em + a.

So: em = in / on / at
a varanda = the balcony / veranda
na varanda = in/on the balcony

Portuguese often contracts em with definite articles:

em + o = no
em + a = na
em + os = nos
em + as = nas

So o vento na varanda literally has the idea of the wind on the balcony / in the balcony area.

Because vento is a masculine singular noun.

So it takes the masculine singular article o: o vento

This does not mean wind is biologically masculine; it is just the grammatical gender of the noun.

Portuguese nouns must match articles and some other words in gender and number, so: o vento forte
not
a vento

Portuguese usually uses estar for a temporary condition or state, and ser for a more permanent or defining characteristic.

Here, the wind being strong is a temporary situation, so estava is the natural choice:

o vento estava muito forte

Using era would sound less natural in this context, because the sentence is describing a passing condition, not an essential characteristic of the wind.

A simple way to think of it: estar = is/was in a certain state
ser = is/was by nature or identity

This is a very common Portuguese pattern.

Fechou is preterite: a completed action.
Estava is imperfect: an ongoing background situation.

So the sentence works like this:

• Minha irmã fechou a cortina = the main action happened and finished
• porque o vento na varanda estava muito forte = the background condition was going on at that time

English often does something similar: My sister closed the curtain because the wind was very strong on the balcony.

So the mix of tenses is not random. It shows:

• one finished action
• one ongoing past situation that explains it

Because muito here is an adverb, not an adjective.

It is modifying forte, and as an adverb it does not change for gender or number: muito forte = very strong

Compare that with muito as an adjective, where it does agree: muita força = a lot of strength
muitas pessoas = many people

So in your sentence: estava muito forte means was very strong, and muito stays the same.

Yes. A minha irmã is also possible.

In Brazilian Portuguese, the article before a possessive can be used or omitted, depending on region, style, and context.

So both of these are possible: Minha irmã fechou a cortina...
A minha irmã fechou a cortina...

Neither changes the basic meaning here. The version without the article is completely natural.

Some Portuguese adjectives have the same form for masculine and feminine. Forte is one of them.

So you get: o vento forte
a chuva forte

The adjective agrees in number, but not in visible gender form here: os ventos fortes
as chuvas fortes

So forte works for both masculine and feminine singular nouns.

A rough pronunciation guide:

minha ≈ MEE-nya
The nh sound is like the ny in canyon.

irmã ≈ eer-MAH̃
The ã is nasal, so the vowel is pronounced through the nose.

fechou ≈ feh-SHOH
The stress is on the last syllable.

A few useful sound notes:

• nh = a palatal nasal sound, like ny
• ch in Brazilian Portuguese usually sounds like sh
• ã is nasal and does not sound like a plain English a

So the sentence has several very typical Brazilian Portuguese sounds in it.