Il neonato dorme nella culla.

Because neonato begins with a normal n sound, so the regular masculine singular article is il.

Italian uses:

• il before most masculine singular nouns: il neonato, il libro
• lo before masculine singular nouns starting with s + consonant, z, ps, gn, x, or y: lo studente, lo zaino
• l' before masculine singular nouns starting with a vowel: l'uomo

So il neonato is the correct form.

It can be both.

In Il neonato dorme nella culla, neonato is being used as a noun, meaning newborn baby / infant.

But it can also be an adjective:

• un bambino neonato is not the most natural phrasing, but structurally it shows adjective use
• more naturally, Italian often simply uses neonato as the noun itself

It comes from the idea of newly born, so it has that adjective-like origin, but in everyday Italian it is very commonly used as a noun.

Because the subject is il neonato, which is third person singular: he/she/it sleeps.

The verb is dormire = to sleep. Its present-tense forms are:

• io dormo = I sleep
• tu dormi = you sleep
• lui/lei dorme = he/she sleeps
• noi dormiamo = we sleep
• voi dormite = you all sleep
• loro dormono = they sleep

So:

• Il neonato dorme = The newborn sleeps

Because in + la normally contracts to nella.

This is very common in Italian:

• in + il = nel
• in + lo = nello
• in + l' = nell'
• in + la = nella
• in + i = nei
• in + gli = negli
• in + le = nelle

So:

• nella culla = in the cradle

You usually do not say in la culla.

Yes. Culla is a feminine singular noun, so it takes:

• la culla = the cradle
• una culla = a cradle

Because it is feminine singular, the combined preposition + article becomes:

• in + la culla = nella culla

Yes, but it means something slightly different.

• Il neonato dorme nella culla = The newborn sleeps in the cradle / The newborn is sleeping in the cradle
• Il neonato sta dormendo nella culla = emphasizes the action as happening right now: The newborn is sleeping in the cradle

In Italian, the simple present dorme is often enough where English might use either sleeps or is sleeping. So the original sentence is completely natural.

Yes. Italian word order is flexible, although the original order is the most neutral one.

Neutral:

• Il neonato dorme nella culla.

You could also say:

• Nella culla dorme il neonato.

That version puts more focus on nella culla or sounds more literary/stylistic. For a basic statement, Il neonato dorme nella culla is the most straightforward choice.

Yes, but it changes the meaning.

• Il neonato dorme nella culla = the newborn sleeps in the cradle
  This refers to a specific newborn.
• Un neonato dorme nella culla = a newborn sleeps in the cradle
  This introduces a newborn that is not specifically identified.

So the grammar is fine either way; the choice depends on whether you mean the or a.

It means in the cradle.

Italian in usually corresponds to in in English. With something like culla, the natural idea is that the baby is inside it or lying in it, so nella culla is the expected expression.

If you wanted on, Italian would usually use su:

• sulla culla = on the cradle

But that would not fit the normal meaning here.

Yes, if you specifically want to mark the baby as female, you could use the feminine form:

• La neonata dorme nella culla.

Changes:

• il → la
• neonato → neonata

The verb dorme stays the same, because it agrees with the subject in person and number, not in grammatical gender.

A simple approximation is:

eel neh-oh-NAH-toh DOR-meh NEL-lah KOOL-lah

A few pronunciation notes:

• il sounds roughly like eel
• neonato has stress on -na-: neo-NA-to
• dorme has stress on dor-
• nella has a doubled ll, so hold the l a little longer
• culla sounds like KOOL-lah, also with a doubled consonant feel

Italian pronunciation is usually quite regular, so once you know the sound rules, sentences like this are very predictable.