Se eu tivesse fechado o zíper antes, o anel não teria caído no chão.

This is a past unreal/counterfactual conditional.

The pattern is:

Se + past perfect subjunctive, conditional perfect

So here you get:

• Se eu tivesse fechado o zíper antes
• o anel não teria caído no chão

It is used for talking about a past situation that did not happen, and an imagined result that also did not happen.

It corresponds to English patterns like:

• If I had closed...
• ...would not have fallen...

Because after se in a past counterfactual sentence, Portuguese normally uses the past perfect subjunctive.

Here:

• tivesse = imperfect subjunctive of ter
• fechado = past participle of fechar

Together, tivesse fechado means had closed.

This is the standard structure:

• Se eu tivesse estudado, teria passado.
• If I had studied, I would have passed.

A very important point: in standard Portuguese, you normally do not say se eu teria fechado in this kind of sentence.

Because teria caído means would have fallen, which refers to a completed event in the past.

• teria caído = conditional of ter
  • past participle
• This is the conditional perfect

By contrast, cairia usually means would fall, not necessarily would have fallen.

So:

• não teria caído = would not have fallen
• não cairia = would not fall

In this sentence, the falling is a completed past event, so teria caído is the natural choice.

Yes, you often can.

Portuguese frequently drops subject pronouns when the verb form already makes the subject clear. So both of these are possible:

• Se eu tivesse fechado o zíper antes...
• Se tivesse fechado o zíper antes...

Including eu can add emphasis or clarity, but it is not always necessary.

Portuguese uses definite articles more often than English.

In this sentence, o zíper and o anel sound natural because they refer to specific, identifiable things in the situation: the zipper and the ring involved.

English often says:

• closed the zipper
• the ring fell

Portuguese does the same here:

• fechado o zíper
• o anel não teria caído

So even though article use is sometimes different between English and Portuguese, in this sentence the articles are very natural.

No chão means on the floor or on the ground, depending on context.

No is a contraction of:

• em + o = no

So:

• no chão = in/on the floor/ground

Portuguese uses these contractions very regularly:

• em + a = na
• em + os = nos
• em + as = nas

So em o chão is not the normal form here; no chão is.

It can mean either one. The exact English translation depends on context.

• indoors, chão often means floor
• outdoors, it often means ground

So in this sentence, if the ring fell inside a room, English would probably say on the floor. But Portuguese still uses no chão naturally.

Here antes means before or earlier.

It refers to doing the zipper-closing earlier than the moment when the ring fell. In other words:

• If I had closed the zipper earlier / beforehand...

Portuguese can use antes by itself when the reference point is understood.

Other natural possibilities would be:

• mais cedo = earlier
• antes disso = before that
• antes de sair = before leaving

But in this sentence, plain antes works perfectly.

Because the i is pronounced separately and is stressed:

• ca-Í-do

The accent shows that aí is not pronounced as one syllable here. This is a common pattern in Portuguese with stressed i or u in hiatus.

Compare:

• caído
• saída
• país

So the accent helps show the correct pronunciation.

No. In this sentence, they do not change.

That is because they are past participles used with the auxiliary verb ter:

• tivesse fechado
• teria caído

After ter, the participle normally stays in the default form.

Compare this with adjectival or passive uses, where agreement does happen:

• A porta estava fechada.
• The door was closed.

But here, with ter, you keep:

• fechado
• caído

regardless of gender or number.

Yes, zíper is very common in Brazil.

It is the normal everyday word for zipper. It comes from English, but it is fully natural in Brazilian Portuguese.

You may also hear other terms in some contexts, but zíper is the safest and most common choice in everyday Brazilian speech.

Yes. The sentence you have is standard and very natural, but you may hear informal variations.

For example:

• Se eu tivesse fechado o zíper antes, o anel não ia ter caído no chão.

Here, não ia ter caído is a common spoken alternative to não teria caído.

You might also hear:

• mais cedo instead of antes

So all of these can be natural, depending on style:

• Se eu tivesse fechado o zíper antes, o anel não teria caído no chão.
• Se eu tivesse fechado o zíper mais cedo, o anel não teria caído no chão.
• Se eu tivesse fechado o zíper antes, o anel não ia ter caído no chão.

For learning and writing, the original sentence is an excellent model.