После разговора нам удалось помириться.

Because после requires the genitive case.

• разговор = nominative singular
• разговора = genitive singular

So:

• после разговора = after the conversation

This is a very common pattern in Russian:

• после урока = after the lesson
• после работы = after work
• после фильма = after the film

So the form разговора is there because of the preposition после.

It means after the conversation or after talking.

The noun разговор means conversation, talk, or discussion. In this sentence, после разговора gives the time context: the reconciliation happened after the talk.

Depending on context, English translations could be:

• After the conversation, we managed to make up.
• After talking, we were able to reconcile.

So it refers to some conversation that helped lead to the result.

Because the verb удаться / удаваться works differently from English manage.

In Russian, удалось is used in an impersonal construction, and the person who succeeds is put in the dative case:

• нам = to us
• мне = to me
• ему = to him
• ей = to her

So нам удалось помириться literally means something like:

• To us, it succeeded to reconcile
• more naturally: We managed to reconcile

This is a very common Russian pattern:

• Мне удалось найти ключи. = I managed to find the keys.
• Им не удалось уйти. = They didn’t manage to leave.

So нам is correct because удалось takes the experiencer in the dative.

Удалось is the past tense, neuter singular form of удаться, a perfective verb meaning:

• to succeed
• to work out
• to manage to

In this sentence, it expresses that something was achieved successfully:

• нам удалось помириться = we managed to reconcile

A useful way to understand it:

• удаваться = imperfective, success as a process/repeated possibility
• удаться = perfective, success as a completed result

Examples:

• Мне удаётся рано вставать. = I manage to get up early. / I’m able to get up early.
• Мне удалось рано встать. = I managed to get up early.

Because удалось normally goes with an infinitive that describes the completed successful action, so the perfective infinitive is very natural here.

• мириться = imperfective
• помириться = perfective

Here, the idea is not just to be reconciling or to be on the way to making peace, but to actually reconcile successfully.

So:

• нам удалось помириться = we managed to reconcile / make up

Using мириться here would sound unusual in most contexts, because удалось points to a successful completed outcome.

They are related but differ in aspect.

мириться — imperfective

This can mean:

• to reconcile
• to make peace
• to be reconciling
• sometimes to put up with depending on context, especially with с чем-то

Examples:

• Они долго мирились. = They were reconciling for a long time.
• Я не хочу мириться с этим. = I don’t want to put up with this.

помириться — perfective

This means:

• to reconcile successfully
• to make up

Example:

• Они наконец помирились. = They finally made up.

So in your sentence, помириться is used because the result matters: the people actually ended up reconciled.

The -ся makes the verb reflexive, but in many Russian verbs that does not mean a literal English reflexive like oneself. Instead, it often forms a verb with a special meaning.

Here:

• мирить = to reconcile someone, to make people reconcile
• мириться / помириться = to reconcile with each other, to make up

So помириться is the natural verb for to make up or to become reconciled.

Compare:

• Мать помирила детей. = The mother reconciled the children.
• Дети помирились. = The children made up.

So -ся here helps create the meaning of the people themselves becoming reconciled.

Because this construction is impersonal.

With удалось / не удалось, Russian often uses a form that is grammatically like it succeeded / it worked out. Since there is no explicit subject like он or она, the past tense appears in the neuter singular form:

• удался = masculine
• удалась = feminine
• удалось = neuter
• удались = plural

In нам удалось помириться, the idea is basically:

• It worked out for us to reconcile
• natural English: We managed to reconcile

So the neuter form is part of the standard impersonal pattern.

Yes, Мы помирились после разговора is perfectly natural.

После разговора нам удалось помириться

This emphasizes the idea of success or difficulty overcome.

It suggests something like:

• reconciliation was not automatic
• it took effort, luck, or a meaningful conversation
• the important point is that they managed to do it

Мы помирились после разговора

This is more neutral and simply states the fact:

• We made up after the conversation

So the original sentence highlights the successful outcome more strongly.

Russian word order is flexible, so putting После разговора first gives it prominence as the setting or background.

The sentence structure is:

• После разговора — time frame
• нам удалось — the successful result
• помириться — the action

Starting with После разговора can feel natural if the speaker wants to emphasize that the conversation was what led to the reconciliation.

Other possible word orders are also grammatical:

• Нам удалось помириться после разговора.
• После разговора удалось нам помириться. — possible, but less neutral

The original order sounds smooth and natural.

They are similar, but not always identical in tone.

• разговор = conversation, talk; very common and neutral
• беседа = conversation, discussion; often a bit more formal, calm, or deliberate

In this sentence, разговор sounds very natural, especially if it was an important talk after some conflict.

For example:

• После разговора нам удалось помириться. = After the conversation, we managed to make up.
• После беседы нам удалось помириться. = also possible, but it may sound a little more formal or deliberate

So разговор is probably the most everyday choice here.

Yes. In many contexts, помириться is the closest Russian equivalent of to make up after an argument.

Examples:

• Мы поссорились, но потом помирились. = We argued, but then we made up.
• Они не могут помириться. = They can’t make up.

So in your sentence, нам удалось помириться is a very natural way to say we managed to make up or we managed to reconcile.