Learn Hardcore Portuguese (Portugal): Temos falado muito sobre gestão do tempo na aula de português. - We have been talking a lot about time management in the Portuguese class.

So Temos falado muito sobre gestão do tempo suggests that over a certain period (e.g. this term, these weeks), in several classes, you’ve been talking a lot about time management.

If you said:

Falámos muito sobre gestão do tempo na aula de português.
→ This sounds more like a completed event in the past (e.g. in yesterday’s class, or at some specific time).

So:

temos falado = focus on ongoing / repeated action up to now
falámos = focus on a finished past event

Is temos falado closer to “we have spoken” or “we have been talking” in English?

In this sentence it’s closer to “we have been talking”:

We have spoken a lot about time management – possible translation, but in English this can sound a bit formal or less obviously ongoing.
We have been talking a lot about time management – better reflects the idea of repeated / continuous discussions up to now.

European Portuguese temos + past participle often matches English “have been + -ing” when it refers to a series of actions or an ongoing situation.

Could I say Estamos a falar muito sobre gestão do tempo instead? What’s the difference?

You can, but the meaning changes slightly:

Temos falado muito sobre gestão do tempo.
→ Over a longer period of time up to now (e.g. this semester), we have repeatedly or regularly talked about time management.
Estamos a falar muito sobre gestão do tempo.
→ Right now / around now, in the current moment or current phase, we’re talking a lot about time management. It feels more like a current ongoing activity, not necessarily something that started long ago.

So:

temos falado = background, accumulated habit over time.
estamos a falar = what’s happening currently (progressive).

Where is the subject “we”? Why don’t we see nós?

In Portuguese, subject pronouns like nós are usually omitted because the verb ending already shows the person:

Temos falado → the -mos ending tells you it’s “we”.

You can say:

Nós temos falado muito sobre gestão do tempo…

This is grammatically correct. You typically use nós if:

you want to emphasise the subject (e.g. Nós temos falado…, not them), or
the context isn’t clear and you want to avoid ambiguity.

But in most neutral contexts, Temos falado… is more natural.

What exactly does gestão do tempo mean, and why is it do and not de?

Gestão do tempo is the standard expression for “time management”.

gestão = management
tempo = time (here, in the sense of time as a resource)
do = contraction of de + o (“of the”)

So literally it’s “management of the time”, but as a fixed phrase it means time management.

Why do and not bare de?

gestão de tempo (without the article) would sound more like “management of time (in general)” and is much less idiomatic.
gestão do tempo refers to the specific notion of time as something you plan and manage in your activities. It’s the usual, idiomatic way to name this concept.

What gender is tempo here, and how do I know do is “de + o”?

Tempo is masculine in Portuguese: o tempo.

When you combine de + o, you get the contracted form do:

de + o tempo → do tempo

Other similar contractions:

de + a → da (da aula)
em + o → no (no tempo)
em + a → na (na aula)

So in gestão do tempo, the o in do tells you the noun is masculine singular.

Why is it na aula de português and not something like em aula de português?

Na aula de português is the natural way to say “in (the) Portuguese class”.

Breakdown:

na = em + a (“in the”)
a aula = the class / lesson
de português = of Portuguese (identifying the subject)

You could see em aula de português in very formal or written contexts, meaning “in (a context of) Portuguese class”, but in everyday speech people almost always say:

na aula de português = in Portuguese class.

Why is it aula de português and not aula em português?

They mean different things:

aula de português
→ a Portuguese class (the subject is Portuguese – you’re learning the language).
aula em português
→ a class given in Portuguese (the language of instruction is Portuguese), but the subject might be something else (history, math, etc.).

In your sentence, the idea is clearly “in Portuguese class (as a school subject)”, so aula de português is correct.

Why is português written with a lowercase p here? Shouldn’t it be Português?

In European Portuguese:

Languages are written with a lowercase letter: português, inglês, francês.
Nationalities as adjectives are also lowercase: aluno português, comida italiana.
Capital letters are used for names of subjects as official course titles in certain formal contexts, but in a normal sentence like this, it stays lowercase.

So aula de português (Portuguese class) is normally written with lowercase p.

What does sobre mean in this context, and could we use de or acerca de instead?

Here, sobre means “about / on the topic of”:

falar sobre gestão do tempo = to talk about time management.

Alternatives:

falar de gestão do tempo
→ Very common too. In many contexts, falar de and falar sobre are interchangeable.
falar acerca de gestão do tempo
→ More formal or literary; also means “talk about”.

In your sentence, all three are grammatically possible:

Temos falado muito sobre gestão do tempo…
Temos falado muito de gestão do tempo…
Temos falado muito acerca de gestão do tempo… (more formal)

Sobre is a very typical choice in neutral speech.

What does muito modify here, and could I say temos muito falado?

In Temos falado muito sobre gestão do tempo, muito is an adverb modifying the verb phrase temos falado. It tells you how much / how often you’ve been talking:

Temos falado muito = We have talked a lot / a great deal.

Can you say temos muito falado?

It’s not wrong grammatically, but it sounds unusual or literary in modern speech.
The standard, natural order in everyday European Portuguese is:
Temos falado muito sobre…

So you should keep muito after the past participle in this kind of sentence.