Se a cola tivesse acabado, nós teríamos esperado a professora, mas ainda havia cola na mesa.

Because in standard Portuguese, an unreal past condition uses this pattern:

• se + imperfect subjunctive
• conditional perfect in the main clause

So:

• Se a cola tivesse acabado = If the glue had run out / had been used up
• nós teríamos esperado = we would have waited

Using teria right after se is not standard in this kind of sentence.

Tivesse acabado is a compound subjunctive form.

It is built with:

• tivesse = imperfect subjunctive of ter
• acabado = past participle of acabar

Together, ter acabado means something like to have ended, to have run out, or to have been used up, depending on context.

So tivesse acabado here means had run out / had been used up.

Teríamos esperado is the conditional perfect, which expresses what would have happened in that hypothetical situation.

It is formed with:

• teríamos = conditional of ter
• esperado = past participle of esperar

So:

• teríamos esperado = would have waited

This matches the English structure very closely.

This is a very common question. In Portuguese, esperar usually takes a direct object:

• esperar alguém = to wait for someone

So:

• esperamos a professora
• esperado a professora

are normal.

In English, you must say wait for someone, but Portuguese does not need for here.

Also, the a in a professora is just the article the, not a preposition.

It is the definite article: the teacher.

So:

• a professora = the teacher

It is not a preposition here, because esperar normally does not require one.

That is why esperar a professora means to wait for the teacher.

Both can express there was / there were in Brazilian Portuguese, but they are a little different in tone.

• havia cola sounds more written, formal, or neutral
• tinha cola is very common in everyday spoken Brazilian Portuguese

So both are possible in many contexts, but havia is often preferred in more careful or written language.

Because the two parts are presenting the noun a little differently.

• a cola refers to a specific glue already understood in the situation
• havia cola is an existential statement: there was glue

With mass nouns like cola, Portuguese often leaves out the article when talking about the mere existence or presence of some amount of it.

So:

• a cola tivesse acabado = if the glue had run out
• havia cola na mesa = there was glue on the table

Yes, but in this context it is better understood as:

• used up
• run out
• gone
• finished

With supplies or substances, acabar often means that something is no longer available.

So a cola tivesse acabado means the glue would have been used up / finished / gone.

Ainda means still here.

In ainda havia cola na mesa, it means:

• there was still glue on the table

Its placement before the verb is very natural and common in Portuguese.

You may also see havia ainda cola na mesa, but ainda havia is the more typical order.

Na is a contraction of:

• em + a = na

So:

• na mesa = on the table or in the table’s location/context, depending on the noun

With mesa, the natural translation is on the table.

This kind of contraction is extremely common in Portuguese:

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

Yes. Portuguese often omits subject pronouns when the verb already makes the subject clear.

So this would also be natural:

• Se a cola tivesse acabado, teríamos esperado a professora, mas ainda havia cola na mesa.

The -íamos ending in teríamos already shows that the subject is we.

Including nós can add a little emphasis or clarity, but it is not necessary.

Cola can mean different things in Brazilian Portuguese, depending on context:

• glue
• cheat sheet
• sometimes even the idea of cheating on a test

In this sentence, cola na mesa strongly suggests the literal meaning glue, especially if the meaning has already been given that way.

So context is what tells you which meaning is intended.