Learn Hardcore Portuguese (Portugal): Um silêncio prolongado pode aumentar a tensão na reunião. - A prolonged silence can increase the tension in the meeting.

Um silêncio prolongado… = A prolonged silence (any such silence, in general)
O silêncio prolongado… = The prolonged silence (a specific one already known from context)

Here, the idea is general: a long silence in a meeting (not a specific, already mentioned one), so um is more natural.

Can I leave out the article and just say Silêncio prolongado pode aumentar a tensão na reunião?

Yes, it’s grammatically possible, but it sounds more like a headline, a title, or a very general statement (almost like a rule or proverb).

Um silêncio prolongado pode aumentar… sounds like normal spoken or written Portuguese.
Silêncio prolongado pode aumentar… is more “headline-like” or stylized.

In everyday sentences, Portuguese usually prefers having an article before singular countable nouns, so um silêncio prolongado is the most natural here.

Why is prolongado after silêncio? Could I say prolongado silêncio?

The default position for most adjectives in Portuguese is after the noun:

silêncio prolongado = literally silence prolonged

You can say prolongado silêncio, but then the adjective sounds more literary, poetic or emphatic, and sometimes slightly changes the feel:

um silêncio prolongado – neutral, standard
um prolongado silêncio – more stylistic, expressive, like something you’d find in literature

For normal, neutral speech, um silêncio prolongado is best.

What’s the difference between prolongado and longo here? Can I say um longo silêncio?

Both are possible, but there’s a nuance:

um silêncio prolongado – a prolonged silence (emphasizes that it was extended in time, longer than expected, or unnaturally long)
um longo silêncio – a long silence (more neutral: it simply lasted a long time)

In many contexts they’re interchangeable, but:

prolongado often suggests that the duration itself is significant or even uncomfortable.
longo is more purely descriptive: it just lasted a long time.

All of these are correct, with slightly different tones:

Um silêncio prolongado pode aumentar a tensão na reunião.
Um longo silêncio pode aumentar a tensão na reunião.

What exactly does pode add here? Why not just Um silêncio prolongado aumenta a tensão na reunião?

Pode is from poder (to be able / can / may) and expresses possibility, not certainty.

Um silêncio prolongado aumenta a tensão… = A prolonged silence increases the tension… (presents it as a general fact)
Um silêncio prolongado pode aumentar a tensão… = A prolonged silence can increase / may increase the tension… (it happens in some cases)

So pode makes the statement less absolute and more like: “This is something that can happen.”

Is the a in a tensão the same as the English to (as in “to increase tension”)?

No. The a in a tensão is the definite article (a = the, feminine singular), not the infinitive marker.

a tensão = the tension (feminine noun with feminine article)
aumentar a tensão = to increase the tension

In Portuguese, the infinitive is just the verb form aumentar, without any separate word like English “to” in front.

Why is it a tensão and not just tensão?

Portuguese tends to use definite articles more than English does, especially with abstract nouns:

English: increase tension
Portuguese: aumentar a tensão

Here, a tensão refers to the tension specific to that meeting. Without the article, aumentar tensão sounds incomplete or unidiomatic in Portuguese in this context. So a tensão is the normal choice.

What does na reunião mean exactly, and where does this na come from?

Na is a contraction:

em (in / at) + a (the, feminine) → na

So:

em a reunião → na reunião = in the meeting / at the meeting

Portuguese always contracts these when spoken and written:

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

Could I say em reunião instead of na reunião?

Yes, but it changes the meaning and usage a bit.

na reunião = in the meeting / at the meeting (a specific meeting)
em reunião = literally in meeting, used more like “in a meeting” as a state or activity, often without specifying which meeting.

Examples:

Estou na reunião. = I am in the (specific) meeting.
Estou em reunião. = I am in a meeting (busy in a meeting, not available).

In your sentence, you’re talking about a specific meeting situation, so na reunião is the natural choice.

Why is reunião feminine (so we use a reunião, na reunião)?

In Portuguese, grammatical gender is largely arbitrary and must be memorized.

reunião ends with -ão, and many -ão nouns are masculine (o avião, o coração), but some are feminine (a reunião, a estação).

There isn’t a reliable, simple rule here; reunião is just one of those nouns you have to learn as feminine:

a reunião
uma reunião
na reunião

Can the word order change to Na reunião, um silêncio prolongado pode aumentar a tensão?

Yes, that’s perfectly correct and very natural.

Na reunião, um silêncio prolongado pode aumentar a tensão.

Putting na reunião at the beginning simply emphasizes the context (“in the meeting”) more. The basic meaning is the same; it’s a matter of focus and style, not grammar correctness.

How would I negate this sentence? Where do I put não?

Place não directly before the verb pode:

Um silêncio prolongado não pode aumentar a tensão na reunião.
= A prolonged silence cannot increase the tension in the meeting.

Pattern:
[subject] + não + [conjugated verb] + [rest of the sentence]

How do I make the sentence plural, talking about multiple prolonged silences?

You need to pluralize the article, noun, adjective, and verb:

Uns silêncios prolongados podem aumentar a tensão na reunião.

Changes:

um → uns (some / a few)
silêncio → silêncios
prolongado → prolongados (agrees with silêncios)
pode → podem (agrees with silêncios)

A tensão and na reunião stay the same because they are still singular.