После короткого разговора нам удалось уладить всё без спора, и я наконец смог отдохнуть.

Because после normally requires the genitive case.

So:

• короткий разговор = a short conversation (dictionary form)
• после короткого разговора = after a short conversation

Both words change to genitive singular:

• короткий → короткого
• разговор → разговора

This is a very common pattern:

• после урока = after the lesson
• после работы = after work
• после встречи = after the meeting

Нам удалось means something like we managed to, we succeeded in, or more literally it turned out successfully for us.

This is a very common Russian structure:

• кому?
  • удалось
• literally: to someone, it succeeded

So:

• нам удалось уладить всё = we managed to settle everything

Grammatically:

• нам is dative plural of мы
• удалось is past tense, neuter singular, from удаться

Russian often uses this kind of impersonal construction where English would simply use a personal subject like we.

Because the verb удаться / удалось does not take its experiencer as a normal subject in the nominative.

Instead, Russian uses the dative:

• мне удалось = I managed to
• тебе удалось = you managed to
• нам удалось = we managed to

So мы удалось is ungrammatical.

Think of it as:

• not we succeeded
• but more like it succeeded for us

Both can often be translated as we managed to settle everything, but they are not identical.

• нам удалось уладить всё emphasizes the successful outcome
• мы смогли уладить всё emphasizes ability / being able

In many contexts they are close, but удалось often sounds a bit more like:

• it worked out
• we succeeded in doing it

while смогли sounds more like:

• we were able to do it

In this sentence, удалось fits well because the focus is that the matter was successfully resolved.

Уладить means to settle, to smooth over, to resolve, especially in a practical or interpersonal situation.

So:

• уладить всё = to settle everything
• уладить конфликт = to resolve a conflict
• уладить проблему = to sort out a problem

It suggests bringing things to a satisfactory conclusion, often calmly or diplomatically.

Because уладить is perfective, and here the speaker is talking about a completed result.

• уладить = to settle / resolve completely
• улаживать = to be settling / to settle repeatedly / in process

Since the sentence describes a finished event in the past, perfective is natural:

• нам удалось уладить всё = we managed to settle everything

If you used улаживать, it would sound wrong here because удалось usually points to a completed successful action.

Because the word here is всё = everything.

This is different from все = all or everyone, depending on context.

Examples:

• всё хорошо = everything is good
• все люди = all people
• все пришли = everyone came

In many Russian texts, ё is often written as е, so you may see все instead of всё, but here the meaning is clearly everything.

Because без requires the genitive case.

So:

• спор = argument/dispute
• без спора = without an argument / without dispute

This phrase means that everything was settled without a quarrel or dispute.

Other examples:

• без проблем = without problems
• без ошибки = without a mistake
• без шума = without noise

No. Без спора does not mean without speaking.

It means without an argument, without a dispute, or without quarrelling.

So the sentence says:

• there was a short conversation
• but it did not turn into an argument

That contrast is important:

• разговор = conversation, talk
• спор = argument, dispute, heated disagreement

They are similar, but they are used for two different actions:

• нам удалось уладить всё = we managed to settle everything
• я наконец смог отдохнуть = I finally was able to rest

So the first part focuses on the success of resolving the situation, and the second part focuses on the speaker finally having the chance/ability to rest.

Using both in one sentence is perfectly natural. Russian often varies such verbs instead of repeating exactly the same structure.

Because смог is the perfective past of смочь, and it emphasizes a successful result: the speaker finally did manage to rest.

Compare:

• я мог отдохнуть = I could rest / I was able to rest / I had the possibility to rest
• я смог отдохнуть = I managed to rest / I succeeded in getting some rest

The word наконец (finally) also strongly supports смог, because it suggests that before this, resting was difficult or impossible.

Because отдохнуть is perfective and means to get some rest, to rest successfully / to have a rest as a completed event.

After смог, Russian often uses the infinitive that best matches the intended meaning:

• смог отдохнуть = managed to get some rest

If you said смог отдыхать, that would sound different and usually less natural here. Отдыхать would focus more on the process or ongoing activity of resting, while отдохнуть fits the idea of finally achieving rest.

Наконец means finally, at last.

It suggests that before this moment, the speaker had been unable to rest, probably because the situation had to be dealt with first.

So:

• я смог отдохнуть = I managed to rest
• я наконец смог отдохнуть = I finally managed to rest

It adds a sense of relief and completion.

Yes. Смог is masculine singular past tense.

So this sentence, as written, suggests the speaker is male.

If the speaker were female, it would be:

• я наконец смогла отдохнуть

This is because Russian past tense verbs agree in gender when the subject is singular.

Because и here connects two clauses, each with its own verbal center:

1. нам удалось уладить всё без спора
2. я наконец смог отдохнуть

In Russian, when и joins two independent clauses, a comma is normally used.

So the comma is not just because of и itself, but because the sentence contains two separate predicative parts.

The word order is natural, but Russian word order is relatively flexible.

The original sentence:

• После короткого разговора нам удалось уладить всё без спора, и я наконец смог отдохнуть.

This order sounds smooth and neutral:

1. time frame first: После короткого разговора
2. main result: нам удалось уладить всё
3. manner: без спора
4. final consequence: и я наконец смог отдохнуть

Some parts could move for emphasis, for example:

• Нам удалось после короткого разговора уладить всё без спора...
• Я смог наконец отдохнуть...

But the original version is very natural and probably the best default phrasing.

Yes:

• После = after
• короткого = short (genitive singular)
• разговора = conversation (genitive singular)
• нам = to us
• удалось = it succeeded / we managed
• уладить = to settle, resolve
• всё = everything
• без = without
• спора = argument, dispute (genitive singular)
• и = and
• я = I
• наконец = finally
• смог = was able / managed (masculine past)
• отдохнуть = to get some rest

A more literal English rendering would be:

• After a short conversation, it was possible for us to settle everything without an argument, and I finally managed to rest.

A more natural English version is:

• After a short conversation, we managed to settle everything without an argument, and I finally got to rest.