Learn Hardcore Latin: Pater rogat: "Cur domi manes et cum amicis non curris?" - Father asks: "Why do you stay at home and not run with your friends?"

Pater is the nominative singular of pater, patris – father as the subject of the verb.
Rogat is he/she/it asks (3rd person singular, present indicative, from rogare).

Latin usually does not use a separate subject pronoun (like he) when the verb ending already shows the person.
So:

pater rogat = father asks or the father asks
The -t ending on rogat tells you the subject is he / she / it.

Why is domi used instead of in domo for at home?

Domi is the locative case of domus (house, home). The locative is a special case used mainly for:

Names of cities and small islands (e.g. Romae = in/at Rome)
A few special nouns such as domus (home), rūs (the countryside)

So:

domi = at home (locative)
in domo = in the house or inside the house (ablative with a preposition)

In this sentence, domi manes means you stay at home, not just physically inside a house building.

What tense and person are manes and curris, and how do we know they both mean you ...?

Both verbs are present indicative, 2nd person singular:

manes – from manēre (to stay, remain)
- Present stem: manē-
- Ending -s → you stay / you are staying
curris – from currere (to run)
- Present stem: curr-
- Ending -is → you run / you are running

In Latin, the ending tells you the subject:

man-es → you stay
curr-is → you run

So there is no need to say tu (you). It is understood from -es and -is.

Why is there no word like you in the Latin question?

Latin regularly drops subject pronouns because the verb ending already indicates the person:

manes and curris both have 2nd person singular endings.
So the meaning you (singular) stay and you (singular) run is built into the verb forms.

You can add tu for emphasis:

Cur tu domi manes et cum amicis non curris?
This would stress you in contrast to someone else (e.g. Why do *you stay at home…?*).

What case is amicis, and why is it used together with cum?

Amicis is ablative plural of amicus, amici (friend).

With cum, the ablative is used to express accompaniment:

cum amicis = with (your) friends

So:

cum
- ablative → with someone
amicis is in the ablative to show that the action curris (you run) happens together with friends.

Can cum go after amicis? I’ve seen forms like amicis cum.

Yes, with nouns like amicis, Latin normally puts cum before:

cum amicis (most common order)

But Latin also allows postposition with cum, especially with pronouns:

mecum = with me (not cum me)
tecum = with you
nobiscum, vobiscum, secum

With regular nouns, amicis cum can occur in poetry or for stylistic reasons, but in ordinary prose cum amicis is standard and natural.

Why is cur at the beginning of the question, and does Latin change word order in questions like English does?

Cur means why and is a question word, so it naturally goes to the front of its clause:

Cur domi manes ... ? → Why do you stay at home … ?

Unlike English, Latin does not need special word order changes like:

English: You stay at home. → Why *do you stay at home?*
Latin: Manes domi. → Cur domi manes?

Latin forms questions by:

Using question words (cur, quid, quis, etc.), or
Adding -ne to a word (e.g. manesne?) for a yes/no question,

but it does not rely on auxiliary verbs or inversion the way English does. Word order is more flexible.

Why is non right before curris and not earlier, like cur non domi manes ...?

Non usually comes immediately before the word it negates, most often the verb:

non curris = you do not run

In this sentence, the father is contrasting two actions:

domi manes – you stay at home
cum amicis non curris – (and) you do not run with (your) friends

So non is put right before curris to negate that particular action.
You could say cur non curris cum amicis? in another context, but here the rhythm and contrast of manes … non curris is clear and natural.

Could the two clauses be reversed, like Cur cum amicis non curris et domi manes? Would that change the meaning?

You can reverse them:

Cur cum amicis non curris et domi manes?

The basic meaning stays the same: Why do you not run with your friends and stay at home?

However, in Latin (as in English) earlier elements are often more prominent. The original order:

Cur domi manes et cum amicis non curris?

starts with the unexpected behavior: staying at home, and then adds the contrast: not running with friends.
If you reverse them, the emphasis slightly shifts to not running with friends as the first focus.

Why is the sentence written as Pater rogat: Cur domi manes et cum amicis non curris? with direct speech, instead of using the subjunctive in an indirect question?

The text uses direct speech:

Pater rogat: Cur domi manes…?
Father asks: Why do you stay at home … ?

Latin also has indirect questions, which use the subjunctive:

Pater rogat cur domi maneas et cum amicis non curras.
Father asks why you stay at home and do not run with your friends.

Difference:

Direct speech: repeats the exact words of the speaker; keeps indicative for real questions.
Indirect question: reports the question as content; uses the subjunctive (here maneas, curras).

The example sentence is simply showing you what the father actually says.

What is the gender and dictionary form of domi, and how does that affect its use?

Domi comes from domus, domus (sometimes domus, -i), which is feminine.

Dictionary form: domus, -us (f.)
Important points:

It is one of the few common nouns that have a locative: domi = at home.
Because it’s a special word with its own locative form, Latin prefers domi rather than in domo when the meaning is “at home” in a general sense.

How would the sentence change if the father were talking to more than one child (you plural)?

You would change the verbs to 2nd person plural:

manes → manetis (you all stay)
curris → curritis (you all run)

So the sentence becomes:

Pater rogat: Cur domi manetis et cum amicis non curritis?
Father asks: Why do you (plural) stay at home and not run with your friends?

The noun amicis is already ablative plural, so it does not need to change.