Miliardo da homoj loĝas tie.

Because miliardo is treated as a regular noun in Esperanto, not as a basic numeral.

So:

• du, tri, dek, cent, mil are number words
• miliono, miliardo are nouns

That is why miliardo has the noun ending -o, and why it is followed by da:

• mil homoj = a thousand people
• miliono da homoj = a million people
• miliardo da homoj = a billion people

As a noun, miliardo can also take normal noun endings if needed, such as -j or -n.

In Esperanto, miliardo means 1,000,000,000.

That is the number modern English usually calls a billion. So:

• miliono = 1,000,000
• miliardo = 1,000,000,000
• biliono = 1,000,000,000,000

So for ordinary English billion, Esperanto normally uses miliardo.

Because da is used after words of quantity, amount, or measure.

So Esperanto says:

• miliardo da homoj = a billion people
• glaso da akvo = a glass of water
• grupo da studentoj = a group of students

De usually shows things like possession, origin, or relationship, not quantity. So da is the correct word here.

No. Homoj is plural because we are talking about many individual people.

After miliardo da, a countable noun is normally plural:

• miliono da steloj = a million stars
• centoj da libroj = hundreds of books
• miliardo da homoj = a billion people

Compare that with mass nouns, which are often singular:

• litro da akvo = a liter of water

Since people are countable, homoj is the natural form.

Because the sentence is making a general statement, not talking about some specific, already known billion people.

So:

• Miliardo da homoj loĝas tie. = A billion people live there.
• La miliardo da homoj loĝas tie. = The billion people live there.
  This would mean a specific billion people already known from context.

In most cases like this, no article is needed.

Loĝi means to live somewhere, to reside, or to dwell.

It is especially used when you are talking about location:

• Mi loĝas en Londono. = I live in London.
• Ili loĝas tie. = They live there.

It is more about where someone lives than about being alive in general.
For general to live as in to be alive or to live one’s life, Esperanto often uses vivi.

So in this sentence, loĝas is the right choice because tie gives a place.

Because Esperanto verbs do not change according to person or number.

So all of these use loĝas:

• mi loĝas = I live
• vi loĝas = you live
• li loĝas = he lives
• ili loĝas = they live
• miliardo da homoj loĝas = a billion people live

The ending -as simply means present tense.

Tie means there.

It is one of the Esperanto correlatives:

• ti- = that / there
• -e = place

So tie literally means in that place / there.

Some related forms are:

• ĉi tie = here
• kie = where
• nenie = nowhere
• ie = somewhere

Because there is no direct object in this sentence.

• Miliardo da homoj is the subject
• loĝas is the verb
• tie is an adverb of place

So no accusative is needed.

A useful comparison:

• tie = there
• tien = to there / thither / to that place

If the sentence involved movement toward a place, you might see -n on the place word.

Yes. Esperanto word order is fairly flexible.

The sentence as written:

• Miliardo da homoj loĝas tie.

is a neutral way to say it.

But you could also say:

• Tie loĝas miliardo da homoj.

That puts more focus on there.

Both are grammatical. The original order is just a straightforward, neutral one.

Yes, absolutely.

• miliardo da homoj already normally means one billion people
• unu miliardo da homoj makes the one explicit

So both are possible:

• Miliardo da homoj loĝas tie.
• Unu miliardo da homoj loĝas tie.

The version without unu is often more natural unless you specifically want to emphasize the number.

A native English speaker should watch two things here:

• ĝ in loĝas is like the sound in measure or vision
• tie has two syllables, not the English word tie

Roughly:

• loĝas ≈ LOH-zhas
• tie ≈ TEE-eh

So tie is ti-e, not one syllable.

A rough full pronunciation of the sentence is:

mee-lee-AR-do da HO-moy LOH-zhas TEE-eh