Изнутри дома было слышно музыку.

Изнутри means from the inside / from within. It points to a source or an outward direction.

• изнутри дома = from inside the house
• внутри дома = inside the house

So:

• Изнутри дома было слышно музыку focuses on the music as coming from within the house
• Внутри дома было слышно музыку would mean that inside the house, music could be heard

That is a very important difference.

Because изнутри can govern the genitive when it is followed by a noun.

So:

• изнутри чего? = from inside what?
• изнутри дома = from inside the house

This is similar to how из also takes the genitive:

• из дома = out of the house / from the house

Here, дома is the genitive singular of дом.

Because this is an impersonal construction.

There is no grammatical subject here. Russian often uses impersonal sentences with words like:

• видно = visible / can be seen
• слышно = audible / can be heard
• холодно = cold

In the past tense, impersonal sentences use the default neuter singular form of to be:

• было видно
• было слышно
• было холодно

So было does not agree with музыку, because музыку is not the subject.

Слышно is not a normal finite verb like слышу or слышал.

It is usually described as a predicative word or a category-of-state word. In practical terms, it means something like:

• it is audible
• can be heard

That is why Russian says:

• слышно музыку = music can be heard
• было слышно музыку = music could be heard

In the present tense, Russian usually omits to be, so you simply say:

• Изнутри дома слышно музыку

Because in this impersonal pattern, the thing being heard is treated like a direct object.

So:

• слышно что? = audible what?
• музыку

That is why you get the accusative:

• музыка → nominative
• музыку → accusative

This is different from a sentence where музыка is the subject.

Yes, absolutely. That is also grammatical.

The difference is in the structure:

1. Изнутри дома было слышно музыку

   • impersonal construction
   • focuses on the fact that music could be heard

2. Изнутри дома была слышна музыка

   • personal construction
   • музыка is now the subject
   • слышна agrees with музыка (feminine singular)

Compare:

• музыка
  • слышна
• песня
  • слышна
• голоса
  • слышны

The second version can sound a bit more descriptive or literary, but both are natural.

Because Russian often does not mention the experiencer if it is not important.

The sentence simply states that the music was audible. It does not say to whom it was audible.

If you want to add that, Russian usually uses the dative:

• Мне было слышно музыку = I could hear the music
• Нам было слышно музыку = We could hear the music

Without that dative phrase, the sentence stays more general and neutral.

It normally describes where the sound was coming from: from inside the house.

So the phrase points to the source of the sound, not the location of the hearer.

If you want to say that the hearer was inside the house, you would more naturally use something like:

• Внутри дома было слышно музыку
• В доме было слышно музыку

So this sentence suggests: the music was audible, and it was coming from within the house.

Yes. Russian word order is flexible, and changing it mostly changes focus or emphasis, not the basic meaning.

For example:

• Изнутри дома было слышно музыку
  Neutral, descriptive; starts with the source

• Музыку было слышно изнутри дома
  Puts more focus on музыку

• Было слышно музыку изнутри дома
  Starts with the impersonal predicate; possible in narration

Because Russian marks grammatical roles with case endings, word order is freer than in English.

In the present tense, Russian usually leaves out to be, so:

• Изнутри дома слышно музыку

That means the same structure, just in the present.

Compare:

• сейчас: Изнутри дома слышно музыку
• в прошлом: Изнутри дома было слышно музыку
• в будущем: Изнутри дома будет слышно музыку

So было is there only because the sentence is in the past.