Из-за шума в коридоре я не расслышал вопрос толком.

Here из-за means because of.

It requires the genitive case, so шум becomes шума.

• шум = noise
• из-за шума = because of the noise

A useful extra note: из-за often introduces a cause, especially one with a negative result, so it fits very naturally with noise causing a problem.

It can also mean from behind in other contexts, but not here.

Because this phrase describes location, not motion.

• в коридоре = in the corridor / hallway
• в коридор = into the corridor

With в:

• where? → usually prepositional case: в коридоре
• where to? → usually accusative case: в коридор

So here the noise is located in the corridor, which is why Russian uses в коридоре.

Расслышать means something like to make out, to catch clearly, or to hear distinctly enough to understand.

So:

• слышать = to hear, to be able to hear
• услышать = to hear, to catch the fact of hearing something
• расслышать = to hear clearly enough to make it out

In this sentence, the idea is not just I did not hear. It is more specifically I couldn’t properly make out what the question was because of the noise.

That is why не расслышал is very natural here.

Расслышал is the past tense masculine singular of the perfective verb расслышать.

Perfective is used because the speaker is referring to a single completed situation: there was a question, and at that moment he failed to catch it properly.

Russian often uses a perfective verb under negation when talking about not managing to achieve a result:

• Я не прочитал письмо. = I didn’t read the letter / I failed to read it.
• Я не понял. = I didn’t understand.
• Я не расслышал вопрос. = I didn’t catch the question.

So the perfective here highlights the unsuccessful result.

Because вопрос is the direct object of the verb, so it is in the accusative case.

For an inanimate masculine noun like вопрос, the accusative singular looks the same as the nominative singular:

• nominative: вопрос
• accusative: вопрос

So the form does not change, even though the case function does.

If the noun were animate, you would often see a different form.

Толком is an adverb meaning something like:

• properly
• clearly
• really
• in a way that makes sense

In this sentence, не расслышал вопрос толком means didn’t properly catch the question or didn’t hear the question clearly enough.

It adds the idea that the speaker maybe heard something, but not well enough to understand it properly.

This word is common in everyday speech.

Examples:

• Я толком не понимаю. = I don’t really understand properly.
• Он толком не объяснил. = He didn’t explain it properly.

Yes, Russian word order is flexible.

This order:

Из-за шума в коридоре я не расслышал вопрос толком.

puts the reason/background first: Because of the noise in the corridor...

That makes the sentence feel natural and context-first.

Other orders are possible, for example:

• Я не расслышал вопрос толком из-за шума в коридоре.
• Я из-за шума в коридоре не расслышал вопрос толком.

These mean basically the same thing, but the emphasis shifts slightly.

Very roughly:

• putting из-за шума в коридоре first foregrounds the cause
• putting я first foregrounds the subject
• putting толком closer to the verb can make the not properly idea stand out more

Yes, it could be omitted if the subject is already clear from context:

• Из-за шума в коридоре не расслышал вопрос толком.

Russian often leaves out personal pronouns when they are obvious.

However, я is perfectly normal here. It can be included:

• for clarity
• for contrast
• simply because the speaker wants the sentence to sound complete and explicit

So both versions are possible.

Yes. In the past tense, Russian verbs agree in gender and number.

• расслышал = masculine singular
• расслышала = feminine singular
• расслышало = neuter singular
• расслышали = plural

So я не расслышал suggests the speaker is male.

If the speaker were female, it would be:

Из-за шума в коридоре я не расслышала вопрос толком.

Not always, but very often it introduces a cause with an undesirable or problematic result.

Examples:

• из-за дождя = because of the rain
• из-за пробок = because of traffic jams
• из-за шума = because of the noise

That is why it sounds especially natural here: the noise caused a problem.

For more neutral causes, Russian may also use other ways to express because of, depending on style and nuance.

Russian has no articles like a or the.

So вопрос can mean either:

• a question
• the question

The context tells you which is more natural.

In many situations, this sentence will be understood as the question, because it sounds like a specific question someone asked. But grammar alone does not mark that distinction.

That is normal in Russian. Context does the job that articles do in English.