A veces, mi hermana y yo discutimos, pero luego nos llevamos bien.

This is a very common confusion.

In Spanish, discutir often means to argue, to quarrel, or to have an argument, especially in everyday speech.

So in this sentence, mi hermana y yo discutimos means my sister and I argue.

A more neutral idea of to discuss is often expressed with verbs like:

• hablar de
• comentar
• debatir (if it is more formal or structured)

So:

• Discutimos mucho = We argue a lot
• Hablamos del problema = We discuss/talk about the problem

Context matters, but in this sentence argue is definitely the right idea.

A veces is a fixed expression meaning sometimes.

You just learn it as a set phrase:

• A veces = sometimes
• Muchas veces = many times / often
• Pocas veces = not often / few times

There is no extra de here. Spanish simply uses a veces as the normal expression.

You can also move it around:

• A veces, mi hermana y yo discutimos.
• Mi hermana y yo a veces discutimos.

Both are natural.

Because mi here is a possessive adjective: my.

• mi hermana = my sister

Mí with an accent is a pronoun, usually used after a preposition:

• para mí = for me
• sin mí = without me

So:

• mi hermana = correct
• mí hermana = incorrect

In normal modern Spanish, possessive adjectives like mi, tu, su, nuestro usually replace the article.

So you say:

• mi hermana
• tu casa
• nuestros amigos

Not:

• la mi hermana
• el tu coche

So mi hermana is exactly what you would expect in standard Spanish.

Both are understandable, but mi hermana y yo sounds more natural and more polite.

Spanish, like English, often puts oneself second in this kind of list.

So:

• Mi hermana y yo = the usual, natural order
• Yo y mi hermana = understandable, but less preferred

It is similar to how English usually prefers my sister and I rather than I and my sister.

Usually, no.

Spanish often leaves out subject pronouns because the verb ending already shows who is doing the action.

• discutimos already tells you it is we
• llevamos here, together with nos, also points to we

So mi hermana y yo discutimos is perfectly complete.

You could add nosotros only for emphasis or contrast:

• Mi hermana y yo discutimos, pero ellos no.
• Nosotros discutimos, pero luego nos llevamos bien.

But in a normal sentence, leaving it out is more natural.

Formally, discutimos can be either:

• present: we argue
• preterite: we argued

The form is the same for nosotros.

So how do you know which one it is? By the context.

Here, A veces means sometimes, so the sentence is talking about a repeated or habitual action. That makes it present tense:

• A veces discutimos = Sometimes we argue

If it were past, you would usually see a past-time clue:

• Ayer discutimos = Yesterday we argued

Because discutir is an -ir verb.

In the present tense, nosotros forms are:

• -amos for -ar verbs
• -emos for -er verbs
• -imos for -ir verbs

So:

• hablar → hablamos
• comer → comemos
• discutir → discutimos

That is why discutemos is wrong.

Llevarse bien is an idiomatic expression meaning:

• to get along well
• to have a good relationship

So:

• Nos llevamos bien = We get along well

This is a very common expression.

Related forms:

• llevarse mal = to get along badly
• se llevan bien = they get along well
• me llevo bien con ella = I get along well with her

It is best to learn llevarse bien as a whole expression, not word by word.

Because llevarse bien is a pronominal expression. The pronoun changes with the subject:

• me llevo bien = I get along well
• te llevas bien = you get along well
• se lleva bien = he/she gets along well
• nos llevamos bien = we get along well
• os lleváis bien = you all get along well
• se llevan bien = they get along well

So the nos is not optional here. It is part of the expression for we.

Without the pronoun, llevar means to carry, to take, or to wear, which is a different verb idea.

In normal Spanish statements, object and reflexive pronouns usually go before a conjugated verb.

So:

• nos llevamos bien = correct

Not:

• llevamosnos bien = incorrect

Pronouns can attach to the end only with:

• an infinitive: queremos llevarnos bien
• a gerund: siguen llevándose bien
• an affirmative command: llevaos bien (Spain)

But with a normal conjugated verb in a statement, the pronoun goes before it.

Because bien is an adverb, and here it describes how they get along.

• nos llevamos bien = we get along well

Bueno / buenos are adjectives, and they describe nouns:

• un buen amigo
• son buenos hermanos

So in this sentence you need the adverb bien, not an adjective.

Here luego means then, afterwards, or later.

So:

• pero luego nos llevamos bien = but then/afterwards we get along well

Yes, después would also work in many contexts:

• pero después nos llevamos bien

That said, luego is very common and natural here, especially in everyday Spanish.

There are two useful punctuation points here:

1. After A veces

   • A veces, mi hermana y yo discutimos...
   • This comma marks a small pause after the introductory expression.
   • It is common, though in short sentences it can sometimes be omitted.

2. Before pero

   • ..., pero luego nos llevamos bien.
   • This comma is standard because pero joins two contrasting clauses:
     • we argue
     • we get along well

So the commas help show the structure and contrast of the sentence clearly.