Learn Hardcore Esperanto: La najbaro loĝas en malnova domo apud nia hejmo. - The neighbor lives in an old house near our home.

You can say la malnova domo or la nia hejmo in some contexts, but then you are being very specific or contrasting it with another one. In this simple sentence, the given form is the most natural.

What is the difference between loĝas and vivas? In English we just say lives.

Esperanto separates two meanings of English live:

loĝi = to reside, to live somewhere, to have one’s home
vivi = to be alive, to live (not be dead), to live one’s life

So:

La najbaro loĝas en malnova domo.
The neighbor lives (resides) in an old house.
Li ankoraŭ vivas.
He is still alive.

You normally use loĝi with prepositions like en, ĉe, apud when talking about address or place of residence.

Could I say Loĝas la najbaro… instead? How strict is the word order?

Word order in Esperanto is flexible, but there is a neutral order:

subject – verb – (rest of the sentence)

So your version:

La najbaro loĝas en malnova domo apud nia hejmo.

is the most neutral and common.

You can say:

Loĝas la najbaro en malnova domo apud nia hejmo.

That puts extra emphasis on loĝas (on the fact of living there). It sounds a bit more poetic or marked, not wrong, just not the plain everyday word order.

In malnova, what does mal- mean?

mal- is a very common prefix in Esperanto that means the opposite of something.

nova = new → malnova = old
bona = good → malbona = bad
alta = tall, high → malalta = short, low
varma = warm → malvarma = cold

So malnova domo literally means non-new house, i.e. old house.

Why is there no -n at the end of domo or hejmo? When do I use the accusative?

The -n ending (accusative) is mainly for:

The direct object of a verb
- Mi vidas la domon. – I see the house.
Showing movement/direction with some prepositions
- Mi iras en la domon. – I go into the house (movement).

In your sentence:

La najbaro is the subject.
loĝas does not take a direct object.
en malnova domo apud nia hejmo describes where he lives; it’s a location, not a direct object.
The prepositions en and apud here indicate a static position (not movement), so no -n is used.

So:

La najbaro loĝas en malnova domo. – The neighbor lives in an old house (no movement).
La najbaro eniras la malnovan domon. – The neighbor enters the old house (movement into → domon).

What is the difference between domo and hejmo? They both look like home/house.

Yes, they are close but not identical:

domo = a physical building for living in → house, home (as a building)
hejmo = home in the emotional/personal sense; the place where you feel at home

So:

Mi revenas hejmen. – I return home. (emotional place)
Mi havas grandan domon. – I have a big house. (the building)

In your sentence:

malnova domo = an old house (a building)
nia hejmo = our home (where we live; may or may not be a single domo)

What exactly does apud mean here? Is it like next to, near, or by?

Apud means close to, next to, by the side of. The distance is usually small.

In your sentence:

apud nia hejmo ≈ near our home / next to our home

Some comparisons:

apud – very near, close by, often directly next to
proksime de – near, in the vicinity of (a bit vaguer)
ĉe – at (someone’s place, at a location, at a person)

Examples:

La lernejo estas apud la parko. – The school is next to the park.
Li loĝas proksime de nia hejmo. – He lives near our home.
Mi loĝas ĉe miaj gepatroj. – I live at my parents’ place.

Why do adjectives like malnova and nia come before the nouns? Can they also come after?

By default, adjectives in Esperanto usually come before the noun:

malnova domo – an old house
nia hejmo – our home

But they can also come after, without changing the basic meaning:

domo malnova
hejmo nia

Possible reasons to put them after:

stylistic/poetic effect
special emphasis or rhythm
in some fixed expressions

You must keep agreement:

singular: malnova domo, domo malnova
plural: malnovaj domoj, domoj malnovaj

How does nia work? Does it change form for plural, like our vs ours?

Nia is a possessive adjective: our.

As an adjective, it agrees with the noun:

nia hejmo – our home
niaj hejmoj – our homes (plural → -j)
nian hejmon – our home (accusative → -n)
niajn hejmojn – our homes (plural + accusative → -jn)

The root is ni- (we), and the -a makes it an adjective: nia = belonging to us.

So in your sentence, nia hejmo is just our home in the normal, singular, non-accusative form.

Is najbaro gender‑neutral? How do I say female neighbor or neighbors?

Yes, najbaro is gender‑neutral by default: a neighbor (person of any gender).

To specify gender:

najbarino – female neighbor (-in- = female)
najbarulo (sometimes) – male neighbor (-ul- = person, sometimes used with context to emphasize male, but many speakers rely on context instead)

Plural:

la najbaroj – the neighbors
la najbarinoj – the (female) neighbors

So:

La najbarino loĝas en malnova domo apud nia hejmo.
The (female) neighbor lives in an old house near our home.

How would I say “The neighbors live in an old house near our home”?

You mainly need to put najbaro in the plural and keep adjective agreement:

La najbaroj loĝas en malnova domo apud nia hejmo.

This means all the neighbors (plural) live together in one old house.

If you want plural houses too:

La najbaroj loĝas en malnovaj domoj apud nia hejmo.
The neighbors live in old houses near our home.

Note that nia hejmo stays singular unless you really mean multiple homes:

apud niaj hejmoj – near our homes (several different homes).