Mihi domum eundum est, quia nox obscura est.

Because this sentence uses the passive periphrastic to express necessity or obligation.

In this construction, the person who has the obligation is often put in the dative case, not the nominative. So:

• mihi = for me / by me / I have to
• eundum est = it must be gone

So Mihi domum eundum est means something like:

• I must go home
• more literally, it must be gone home by me

That literal English is awkward, but it helps show how the Latin works.

Eundum est is an example of the gerundive of obligation (also called the passive periphrastic).

It is made from:

• eundum — the gerundive of eo, ire (to go)
• est — is

Together they mean:

• it must be gone
• more naturally, one must go or must go

Since eo is an intransitive verb (to go does not take a direct object), Latin often uses this construction impersonally, in the neuter singular:

• eundum est = it is necessary to go

Then mihi tells us who has to do it.

Because the construction is impersonal.

When a passive periphrastic is built from an intransitive verb like eo, there is no direct object for the gerundive to agree with. So Latin commonly uses the neuter singular as a kind of default form:

• eundum est = it must be gone / one must go

If there were a noun for the gerundive to agree with, it would match that noun in gender, number, and case. But here there is no such noun, so the neuter singular is used.

Because Latin often uses certain place words, especially domus (home/house), without a preposition to show motion toward them.

So:

• domum = home, to home, homeward

This is an example of the accusative of place to which without a preposition.

Compare:

• domum ire = to go home
• but with most ordinary nouns, Latin would use ad
  • accusative:
    • ad urbem ire = to go to the city

So domum is a special and very common idiom.

Yes. Domum is the accusative singular of domus.

In this sentence it expresses motion toward home. Even though English just says home, Latin treats it as a directional accusative.

Related forms are useful to know:

• domus = home/house (nominative)
• domum = homeward / to home
• domi = at home
• domo = from home

These are very common and slightly irregular uses of domus.

No, not in standard classical Latin for this meaning.

When Latin wants to say I must go home, it typically uses the gerundive of obligation:

• Mihi domum eundum est

It does not normally use an infinitive with est in that way. So ire est would not be the normal idiom here.

The important pattern to learn is:

• dative of the person
  • gerundive
    • sum

So:

• mihi eundum est = I must go
• tibi faciendum est = you must do it
• nobis laborandum est = we must work

Quia means because.

It introduces the reason:

• Mihi domum eundum est = I must go home
• quia nox obscura est = because the night is dark

So the whole sentence means:

• I must go home, because the night is dark.

It is a straightforward subordinating conjunction connecting the main clause to a clause of cause.

Nox obscura est is a simple and natural way to say the night is dark.

Here:

• nox is the subject, nominative singular
• obscura is an adjective agreeing with nox
• est is the verb

Because nox is feminine singular, the adjective must also be feminine singular:

• nox obscura

Latin word order is flexible, so you might also see:

• obscura nox est
• nox est obscura

But nox obscura est is perfectly normal and easy to understand.

Because it agrees with nox, which is a feminine noun.

In Latin, adjectives must agree with the nouns they describe in:

• gender
• number
• case

So:

• nox = nominative singular feminine
• obscura = nominative singular feminine

That agreement shows that obscura describes nox.

It says the night is dark.

That is because obscura is being used as a predicate adjective, not just as an attributive adjective.

So:

• nox obscura est = the night is dark

If Latin wanted simply the dark night, without is, it could say:

• nox obscura

But with est, the meaning is clearly the night is dark.

Yes, but the literal translation is awkward in English.

A very literal version would be:

• To me, it must be gone home
• or Home must be gone to by me

That sounds unnatural in English, but it helps reveal the grammar:

• mihi = the person under obligation
• domum = direction toward home
• eundum est = it must be gone

The best natural translation is simply:

• I must go home

The tense comes from est, which is present. So the sentence expresses a present necessity:

• I must go home
• I have to go home

It does not by itself specify exactly when the action will happen, only that the obligation exists now.

If Latin changed est to another tense, the sense of necessity would shift too. For example:

• mihi eundum erat = I had to go
• mihi eundum erit = I will have to go

So here the idea is a present one: the speaker currently needs to go home.

Yes. It is a very common and idiomatic Latin way to express necessity.

Latin often uses:

• dative of person
• • gerundive
• • a form of sum

So for many verbs, especially in formal or literary Latin, this is a standard pattern:

• mihi hoc faciendum est = I must do this
• nobis laborandum est = we must work
• tibi domum eundum est = you must go home

So this sentence is a good example of a major Latin construction worth learning well.