Vocea ei este liniștită.

Because vocea means the voice, while voce just means voice.

Romanian usually puts the definite article at the end of the noun:

• voce = voice
• vocea = the voice

So vocea is the noun voce with the attached definite article -a.

In Romanian, when a noun is followed by a possessor, the noun is usually made definite.

So:

• vocea ei = her voice
• literally, this is closer to the voice of her

This is very normal Romanian structure:

• cartea mea = my book
• casa lui = his house
• vocea ei = her voice

So the definite form here is exactly what you should expect.

Here, ei means her.

In this sentence, it shows possession:

• vocea ei = her voice

A more literal breakdown is:

• vocea = the voice
• ei = of her

So ei comes after the noun and tells you who the voice belongs to.

Here ei is in the genitive role, because it shows possession.

So in vocea ei, ei means of her:

• vocea ei = her voice

If you are not focusing on case terminology yet, the important thing is simply:

• after a noun, ei can mean her / of her

Because liniștită has to agree with vocea, and vocea is feminine singular.

Romanian adjectives agree with the noun they describe:

• masculine singular: liniștit
• feminine singular: liniștită

Since vocea is feminine singular, the adjective must also be feminine singular:

• Vocea ei este liniștită.

It agrees with vocea, not with ei.

That is an important point:

• vocea is the noun being described
• ei only tells you whose voice it is

So the adjective matches voice, not her.

Este is the full 3rd person singular form of a fi (to be), so it means is.

• este = is
• e = a shorter, very common spoken form of este

So both are possible:

• Vocea ei este liniștită.
• Vocea ei e liniștită.

The first sounds a bit more neutral or formal; the second is very common in everyday speech.

Usually no, not in a normal full sentence like this.

• Vocea ei este liniștită. = complete sentence
• Vocea ei liniștită. = sounds incomplete, more like a fragment

Romanian normally keeps the verb to be in this kind of sentence.

Vocea ei este liniștită is the most neutral, standard word order.

You can also hear:

• Vocea ei e liniștită.

Other word orders are possible for emphasis or style, but they are less neutral. For a learner, Vocea ei este liniștită is the safest pattern to use.

A rough English-friendly pronunciation is:

VO-chea ey ES-te lee-neesh-tee-TUH

A few useful sound notes:

• ce in vocea sounds like che in check
• ei sounds roughly like ay
• ș sounds like sh
• ă is a short neutral vowel, like uh

So:

• vocea ≈ VO-chea
• ei ≈ ay
• liniștită ≈ lee-neesh-tee-TUH

Yes, you could.

• vocea ei = her voice
• vocea sa = his/her voice

The difference is that sa can be more ambiguous, because it can mean his or her, depending on context. Ei makes it clearly her.

In everyday speech, many speakers prefer ei when they want to be specific:

• vocea ei = definitely her voice