Nocte tranquilla tertia vigilia pauci adhuc in turri manent, ceteri autem dormiunt.

Because Latin often uses the ablative without a preposition to express time when. So:

nocte tranquilla = on a calm night
tertia vigilia = at the third watch

Both phrases set the time of the action. The adjectives agree with their nouns in case, number, and gender: tranquilla with nocte, and tertia with vigilia.

No. It is better understood as an ablative phrase of time/circumstance, not an ablative absolute.

A true ablative absolute usually has a noun plus a participle, such as urbe capta (with the city having been captured / after the city was captured). Here there is no participle, just a noun and adjective: nocte tranquilla.

So this simply means on a calm night.

It refers to a Roman way of dividing the night. The night was commonly divided into four watches (vigiliae). So tertia vigilia means the third watch of the night.

Roughly speaking, that would be around midnight to 3 a.m., though exact times could vary.

So this phrase does more than just say at night; it gives a more precise time within the night.

Grammatically, tranquilla could match either noun, because both nocte and vigilia are feminine singular ablative. But in this sentence it is naturally understood with nocte.

There are two main reasons:

First, nocte tranquilla is a very natural phrase: on a calm night.
Second, tertia vigilia is a standard expression meaning at the third watch.

So the sentence is best read as two time phrases:

nocte tranquilla
tertia vigilia

They are originally adjectives, but here they are being used substantively, meaning they stand on their own like nouns.

So:

pauci = a few
ceteri = the others or the rest

An implied noun is understood, such as men, soldiers, or guards, depending on context.

Both are nominative masculine plural here, because they are the subjects of manent and dormiunt.

Adhuc means still, yet, or up to this point.

Here it emphasizes that even now, at this late hour, a few are still in the tower. It gives a sense of continuation: they have not left or gone to sleep yet.

So pauci adhuc in turri manent suggests something like a few are still remaining in the tower.

Because in takes:

the ablative when it means in/on a place, showing location
the accusative when it means into/onto a place, showing motion toward

Here the men are in the tower, not moving into the tower, so Latin uses the ablative:

in turri = in the tower

If the sentence meant they go into the tower, then you would expect in turrim.

Because autem is a postpositive word. That means it usually comes second in its clause, not first.

So Latin prefers:

ceteri autem dormiunt

rather than putting autem first.

This is very common with words like autem, enim, and vero. In English we usually translate autem as but, however, or on the other hand.

Both are third person plural present active indicative verbs.

manent = they remain / they stay
dormiunt = they sleep / they are sleeping

Their subjects are:

pauci for manent
ceteri for dormiunt

So the sentence contrasts two groups doing two different things.

Because manent is more specific than sunt.

sunt would simply mean are: it states presence.
manent means remain or stay: it suggests continued presence, often with the idea that others are no longer there or that they are staying on duty.

So pauci adhuc in turri manent is stronger than pauci in turri sunt. It suggests that a few are still remaining there.

Latin word order is much freer than English word order because the endings show the grammatical relationships.

This sentence is arranged in a very natural Latin way:

Nocte tranquilla tertia vigilia — time setting first
pauci adhuc in turri manent — first group and what they are doing
ceteri autem dormiunt — contrasting group and what they are doing

So the order helps highlight the contrast:

a few are still in the tower,
but the rest are asleep.

Because Classical Latin does not have articles like English the or a/an.

Latin usually leaves definiteness to context. So:

pauci can mean a few
ceteri can mean the rest
in turri can mean in the tower

English has to add articles, but Latin does not.