Learn Hardcore Portuguese (Portugal): A televisão está com o volume baixo; não consigo ouvir. - The television has the volume low; I can’t hear.

estar com + noun + adjective is very natural in Portuguese to describe a temporary state or condition: the TV is currently with low volume.
tem o volume baixo is also correct; it sounds a bit more neutral/static.
o volume está baixo is the most direct: it makes the volume the subject. All three are fine here; choice is about focus and style.

Can I drop the article and say está com volume baixo?

You can, but com o volume baixo is more idiomatic when referring to the specific TV’s volume. Without the article feels a bit more generic (like “with low volume” in general).

Why is the adjective after the noun (volume baixo) and not baixo volume?

Portuguese typically places adjectives after nouns. Baixo volume can occur in set phrases/technical contexts, but the everyday, natural order here is volume baixo.

Could I say o som instead of o volume?

Yes:

o volume = the setting/level on the device.
o som = the sound itself (output). Both are common: A televisão está com o som baixo is perfectly idiomatic too.

Is televisão the device or the medium? What about TV or televisor?

In Portugal, a televisão commonly refers to the device in everyday speech.
a TV (said “tê-vê”) is very common and also feminine.
o televisor exists but sounds more formal/technical. Grammatical gender: televisão/TV = feminine; televisor = masculine.

What’s the difference between não consigo ouvir, não posso ouvir, and não ouço?

não consigo ouvir = I’m unable to hear (lack of ability in the moment).
não posso ouvir = I can’t (not allowed/it’s not possible for external reasons).
não ouço = I don’t hear/I can’t hear (simple present statement of fact; less emphasis on the reason).

What’s the nuance between ouvir and escutar in European Portuguese?

ouvir is the default verb and covers both hearing and listening in most contexts.
escutar implies purposeful, attentive listening. You can use it, but ouvir is more common here.

If I want to say “I can’t hear it,” how do I add the pronoun?

Two natural options in EP:

Não a consigo ouvir. (proclisis because of the negative não)
Não consigo ouvi-la. (attach the pronoun to the infinitive) Use -la for a feminine antecedent (a televisão), -lo for a masculine one (o som). Avoid lhe here; lhe is indirect object, not used for direct objects like “it.”

Is the semicolon (;) necessary here? Could I use a comma or a conjunction?

The semicolon neatly links two closely related clauses. You could also write:

A televisão está com o volume baixo. Não consigo ouvir.
A televisão está com o volume baixo, por isso não consigo ouvir.
Or invert with porque: Não consigo ouvir porque a televisão está com o volume baixo.

Could I say está no volume baixo?

Not for “low volume” in general. Use:

está com o volume baixo or o volume está baixo. Say no volume cinco when referring to a specific level: “it’s on volume five.”

Any other natural ways to express the second clause?

Yes:

Não estou a ouvir. (I’m not hearing right now; EP progressive)
Não dá para ouvir. (It’s not possible to hear)
Não consigo ouvir bem / nada. (I can’t hear well / at all)

Pronunciation tips (European Portuguese)?

Approximate EP pronunciation:

A [ɐ] (like a quick “uh”)
televisão [tɨlɨviˈzɐ̃w̃] (“tuh-luh-vee-ZOWN,” final nasal “ão”)
está [ʃˈta] (often “shtá”)
com [kõ] (nasal “on”)
o [u] (“oo”)
volume [voˈlum(ɨ)] (“vo-LOOM(uh)”)
baixo [ˈbajʃu] (“BAY-shoo”)
não [nɐ̃w̃] (nasal “nãw”)
consigo [kõˈsiɣu] (“kõ-SEE-goo,” soft “g”)
ouvir [oˈviɾ] (“oh-VEER,” tapped r)

Does com contract with the article here? Why isn’t it co?

com doesn’t contract with the definite article; it stays com o / com a. (It does fuse with pronouns: comigo, contigo, connosco/conosco, convosco.)

Could I use em baixo/abaixo instead of baixo?

No for volume. Use baixo (adjective): o volume está baixo.
em baixo means “down/below (location),” and abaixo means “below/under,” not used for volume level.

Any chance of confusion with consigo meaning “with you/him/her”?

Context disambiguates it. Here, consigo is the verb conseguir (I manage/can). The prepositional form meaning “with you (formal)/him/her/them” only appears after com (e.g., falo consigo = “I speak with you, sir/ma’am”).