Learn Hardcore Croatian: Sinoć su se brat i sestra pomirili nakon rasprave. - Last night the brother and sister made up after a discussion.

So su se is correct; se su breaks this fixed order and sounds wrong to native speakers.
You also cannot start the sentence with se (Se sinoć brat i sestra pomirili is ungrammatical).

Why is the verb pomirili masculine plural, even though one person is female (sestra)?

Croatian agreement rules say:

If the group is all female, use feminine plural.
If the group is mixed (at least one male), the default is masculine plural.

Here the subject is brat i sestra (brother + sister), a mixed group, so the past participle is masculine plural:

brat i sestra su se pomirili (mixed → masc. plural)
dva brata su se pomirila (special case with braća, see below)
dvije sestre su se pomirile (all female → fem. plural)

So pomirili is the normal, grammatically required form here.

Why do we need se? Can we say Sinoć su brat i sestra pomirili nakon rasprave?

No, you can’t just drop se here, because it changes the meaning:

pomiriti se = to reconcile, to make up (with someone) – reflexive
pomiriti (nekoga) = to reconcile someone (else), to bring someone to terms – non‑reflexive

In Sinoć su se brat i sestra pomirili, se marks that they reconciled with each other (reciprocal meaning).

If you say Sinoć su brat i sestra pomirili nakon rasprave, it sounds incomplete: Last night the brother and sister reconciled (someone) after the argument. Native speakers would expect an object:

Sinoć su brat i sestra pomirili roditelje nakon rasprave.
Last night the brother and sister reconciled their parents after the argument.

So se is essential to express they made up (with each other).

What tense is su se pomirili and how is it formed?

This is the past tense (perfekt) in Croatian.

It is formed with:

The present tense of biti (to be) as an auxiliary:
- sam, si, je, smo, ste, su
The past participle of the main verb:
- pomirio / pomirila / pomirili / pomirile…

So:

Oni su se pomirili. – They reconciled / they have reconciled.

In your sentence:

Subject: brat i sestra → oni (3rd person plural)
Auxiliary: su
Past participle (masc. plural): pomirili
Reflexive clitic: se (placed inside the auxiliary–participle pair)

Together: su se pomirili = reconciled (they did).

Why is it brat i sestra and not brata i sestru?

Because brat i sestra is the subject of the sentence, so it must be in the nominative case.

brat (nom. sg.) – brother
sestra (nom. sg.) – sister

If they were the object, you would use the accusative:

Vidim brata i sestru. – I see the brother and (the) sister.
(brata, sestru = accusative)

But in Sinoć su se brat i sestra pomirili nakon rasprave, who reconciled?
→ brat i sestra → subject → nominative.

What case is rasprave, and why is it used here?

Rasprave here is genitive singular of rasprava (discussion, argument).

nominative: rasprava
genitive: rasprave

The preposition nakon (after) always takes the genitive case:

nakon rasprave
nakon svađe
nakon ručka
nakon posla

So nakon rasprave literally means after (the) argument/discussion in genitive.

What is the difference between rasprava and svađa?

Both can be translated as some kind of argument, but they differ in nuance:

rasprava
- basic meaning: discussion, debate
- can be neutral or formal (e.g. parlamentarna rasprava – parliamentary debate)
- can also mean a heated discussion/argument, depending on context
svađa
- clear negative tone: quarrel, row, fight (verbal)
- strongly suggests anger, raised voices, conflict

In your sentence, nakon rasprave can mean after their argument, but it sounds a bit milder than nakon svađe. If you want to stress a serious fight, nakon svađe is stronger emotionally.

What is the difference between sinoć and jučer navečer?

Both refer to last night, but:

sinoć = last night (the night just before today)
- one word, very common and neutral
- usually enough on its own
jučer navečer = yesterday evening
- literally: yesterday in the evening
- also natural, maybe a touch more “descriptive”

In practice:

Sinoć su se brat i sestra pomirili. – very natural, standard.
Jučer navečer su se brat i sestra pomirili. – also fine, slightly more explicit about the evening.

Sinoć navečer is generally redundant; most people just say sinoć.

Can the word order be changed? For example: Brat i sestra su se sinoć pomirili nakon rasprave?

Yes. Croatian word order is relatively flexible, but clitics (like su, se) have restrictions.

All of these are fine and common, with slightly different emphasis:

Sinoć su se brat i sestra pomirili nakon rasprave.
(focus a bit on last night)
Brat i sestra su se sinoć pomirili nakon rasprave.
(neutral, subject first, then time)
Brat i sestra su se pomirili sinoć nakon rasprave.
(emphasis more on the act of reconciling, when added later)

What you cannot do is move se or su freely:

✗ Sinoć se su brat i sestra pomirili… – wrong order of clitics
✗ Sinoć brat i sestra su se pomirili… – here su se should come immediately after the first stressed word (Sinoć), not after brat i sestra.

Rule of thumb: after the first meaningful word/phrase, put the whole clitic cluster (su se) together.

How would the sentence change if the siblings were both sisters or both brothers?

Two sisters (all female)
Subject is feminine plural → verb agrees in feminine plural:
- Sinoć su se sestre pomirile nakon rasprave.
  Last night the sisters reconciled after the argument.
Here, pomirile ends in -e, marking feminine plural.
Two brothers
The usual noun for “brothers (as a group)” is braća, which behaves as a neuter plural in agreement:
- Sinoć su se braća pomirila nakon rasprave.
  (past participle pomirila, neuter plural, like with djeca – children)
If you explicitly say dva brata, speakers often still use pomirila by attraction to braća, but in everyday speech you may also hear masculine plural pomirili. The safest textbook version with the collective noun is:
- Braća su se pomirila.

How would you say “They reconciled with their parents” using pomiriti se?

You use pomiriti se s + instrumental (to reconcile with someone).

Pomirili su se s roditeljima.
They reconciled with their parents.

If you want to keep the “last night, after the argument” context:

Sinoć su se pomirili s roditeljima nakon rasprave.
Last night they reconciled with their parents after the argument.

Is nakon always followed by the genitive, and can I use poslije instead?

Yes:

nakon always takes the genitive:
- nakon rasprave
- nakon ručka
- nakon posla
poslije also takes the genitive when it has an object:
- poslije rasprave
- poslije ručka

In your sentence you can say:

Sinoć su se brat i sestra pomirili nakon rasprave.
Sinoć su se brat i sestra pomirili poslije rasprave.

Both are correct.
nakon may sound a bit more formal or “bookish”; poslije is very common in everyday speech.

Note: poslije can also be used on its own as an adverb:

Pomirili su se poslije. – They made up later.

Why is rasprave singular if in English we might say “after arguments” in the plural?

Croatian often uses a singular noun where English might use a plural for repeated or generic events.

nakon rasprave – after the argument / the discussion (one event)
nakon rasprava – after (a series of) arguments/discussions (clearly plural)

In your sentence, nakon rasprave presents it as one specific argument/discussion that happened before they reconciled. If you really want to stress that there were many separate arguments, you can say:

Sinoć su se brat i sestra napokon pomirili nakon mnogih rasprava.
Last night the brother and sister finally reconciled after many arguments.