En el sótano casi no hay cobertura, así que no pude descolgar ni escuchar bien el mensaje.

Yes. En el sótano means in the basement.

• en = in
• el sótano = the basement

Spanish often starts a sentence with a place phrase like this to set the scene: In the basement, there’s almost no signal...

It means there is almost no signal / coverage.

Breakdown:

• casi = almost
• no hay = there isn’t / there is not
• cobertura = coverage, especially mobile phone signal/reception

So casi no hay cobertura literally means there is almost no coverage, but in natural English you would often say there’s almost no signal.

In Spain, cobertura is very commonly used for mobile reception.

Because hay is used to say that something exists or is present.

• hay cobertura = there is coverage
• no hay cobertura = there is no coverage

You would not say está cobertura because cobertura is the thing that exists in that place; you are not describing where coverage is located as a normal object.

This is the same pattern as:

• Hay gente = There are people
• Hay ruido = There is noise
• Hay señal = There is signal

Because casi no works together as a unit meaning hardly any / almost none / almost not.

So:

• casi no hay cobertura = there is hardly any coverage

If you moved casi, the meaning or naturalness would change. Casi no hay is the normal and natural order.

Very similar examples:

• Casi no tengo tiempo = I hardly have any time
• Casi no habla = He/She hardly speaks

Así que means so, therefore, or which is why.

It connects the cause and the result:

• En el sótano casi no hay cobertura = cause
• así que no pude... = result

So the whole idea is: There’s almost no signal in the basement, so I couldn’t...

It is very common in spoken and written Spanish.

Because no pude is the preterite of poder, and it refers to a completed specific situation in the past: at that moment, the speaker was unable to do it.

• no pude = I couldn’t / I was unable to
• no podía = I couldn’t / I wasn’t able to, but more as a background state, repeated situation, or ongoing circumstance

Here, the sentence is talking about one concrete result: because there was almost no signal, the speaker couldn’t answer or hear the message properly. That makes no pude the most natural choice.

Compare:

• Ayer no pude llamarte = Yesterday I couldn’t call you
  one specific event

• Cuando vivía allí, no podía usar el móvil en el sótano = When I lived there, I couldn’t use my phone in the basement
  habitual or ongoing past situation

Literally, yes: descolgar can mean to take down, to unhang, or to remove from where it is hanging.

But in phone-related Spanish, especially in Spain, descolgar also means to answer the phone.

This comes from older telephones, where you physically lifted the receiver off the hook.

So here:

• no pude descolgar = I couldn’t answer the phone

This is very common in Spain. In other varieties of Spanish, learners may also hear:

• contestar el teléfono
• responder al teléfono

But descolgar is very idiomatic in Spain.

Because ni is used after a negative idea to mean nor or not even.

So:

• no pude descolgar ni escuchar bien el mensaje
  = I couldn’t answer the phone nor hear the message properly = more naturally, I couldn’t answer the phone or hear the message properly

After a negative verb, Spanish often uses ni where English would usually use or:

• No tengo tiempo ni dinero = I have neither time nor money
• No vino ni llamó = He/She neither came nor called

So ni is exactly what you would expect after no pude.

In natural English here, it means hear the message clearly or make out the message properly.

Word-for-word:

• escuchar = to listen / to hear
• bien = well
• el mensaje = the message

But because the context is poor signal, the real idea is that the speaker could not hear or understand the message properly.

Depending on context, mensaje could be:

• a voice message
• part of a phone call
• a voicemail-type message

Because el mensaje refers to a specific message, one that the speaker and listener can identify from the situation.

• el mensaje = the message
• un mensaje = a message

In this sentence, it sounds like there was one particular message involved, so el mensaje is the natural choice.

You can use cobertura widely, and it will be understood across the Spanish-speaking world, but it is especially common in Spain for mobile coverage / signal.

In everyday speech, people may also say things like:

• señal = signal
• No hay señal = There’s no signal

In Spain, no hay cobertura sounds very natural and standard.

Yes. A few natural alternatives are:

• En el sótano casi no hay señal, así que no pude contestar ni oír bien el mensaje.
• En el sótano no había casi cobertura, así que no pude coger la llamada ni escuchar bien el mensaje.
• En el sótano casi no se coge cobertura, así que no pude descolgar ni oír bien el mensaje.

Some notes:

• señal is a very common alternative to cobertura
• contestar is a more general verb for answer
• coger la llamada is common in Spain, but learners should remember coger has different slang associations in some Latin American countries
• oír and escuchar can both work here, though oír often feels especially natural for simply hearing a sound

It breaks down like this:

• En el sótano = place
• casi no hay cobertura = situation/problem
• así que = connector meaning so
• no pude = past result (I couldn’t)
• descolgar ni escuchar bien el mensaje = the two actions the speaker could not do

So the pattern is:

place + problem + so + past inability + two infinitives

That is a very common and useful structure in Spanish.