Después de la conversación, me sentí más tranquilo.

Después often means after / afterwards, but when it is followed by a noun or an infinitive, Spanish normally uses de:

• después de la conversación = after the conversation
• después de comer = after eating

If después stands alone, then de is not needed:

• Hablamos y después me fui. = We talked and afterwards I left.

Spanish often uses the definite article more naturally than English does. In this sentence, la conversación refers to a specific conversation already understood from context, so the conversation is the natural choice.

Spanish could also say:

• Después de nuestra conversación = After our conversation

But la conversación is completely normal if both speakers already know which conversation is meant.

The verb here is sentirse, which means to feel in the sense of emotional or personal state.

So:

• me sentí = I felt
• te sentiste = you felt
• se sintió = he/she/you felt

This is a reflexive verb in Spanish, even though English does not say I felt myself in this context.

Compare:

• sentir = to feel something
  
  • Siento frío. = I feel cold.
• sentirse = to feel a certain way
  
  • Me siento cansado. = I feel tired.

Sentí is the preterite, which presents the feeling as a completed event or change at a specific moment in the past.

• Después de la conversación, me sentí más tranquilo.
  = After the conversation, I felt calmer.

This suggests a change happened as a result of the conversation.

If you said me sentía más tranquilo, that would sound more like an ongoing state or background feeling in the past:

• Después de la conversación, me sentía más tranquilo durante unas horas.
  = After the conversation, I was feeling calmer for a few hours.

So in your sentence, sentí is used because the speaker is describing the result of that conversation.

Adjectives in Spanish usually agree with the person they describe.

Here, tranquilo describes the speaker, the I in me sentí. So:

• tranquilo = used by a male speaker
• tranquila = used by a female speaker

So a female speaker would say:

• Después de la conversación, me sentí más tranquila.

Más tranquilo means calmer or more relaxed. It is a comparison with the speaker’s earlier state.

• tranquilo = calm
• más tranquilo = calmer / more calm

So the sentence implies:

• before the conversation, the speaker was less calm
• after the conversation, the speaker felt calmer

Yes, in many contexts you can, but más tranquilo is often the more natural and common choice for a person feeling emotionally calmer or more at ease.

• tranquilo often suggests calm, relaxed, reassured
• calmado can also mean calm, but sometimes sounds a bit more like settled down

In this sentence, más tranquilo is very natural.

The phrase Después de la conversación is an introductory time expression. A comma after that kind of phrase is very common, especially in writing, because it separates the setting from the main clause:

• Después de la conversación, me sentí más tranquilo.

In informal writing, people may sometimes omit the comma, but using it is good style.

Yes. Tras also means after and is a little more concise:

• Tras la conversación, me sentí más tranquilo.

Both are correct.
Después de is very common and transparent for learners, while tras can sound a bit more formal or literary depending on context, though it is perfectly normal.

Because the sentence focuses on feeling calmer, not simply being calmer.

• me sentí más tranquilo = I felt calmer
• estuve más tranquilo = I was calmer
• estaba más tranquilo = I was calmer / I used to be calmer / I was feeling calmer, depending on context

Spanish often uses sentirse when talking about someone’s emotional or internal state. It matches English felt very well here.

Very often, yes. Sentirse is commonly followed by an adjective or a similar expression describing a state:

• Me siento cansado. = I feel tired.
• Se sintió feliz. = He/She felt happy.
• Nos sentimos mejor. = We felt better.

It can also be followed by nouns in some expressions, but adjectives are extremely common.

The infinitive is sentirse.

In the preterite, it goes like this:

• me sentí = I felt
• te sentiste = you felt
• se sintió = he/she/you felt
• nos sentimos = we felt
• os sentisteis = you all felt (Spain)
• se sintieron = they/you all felt

Notice that sentirse changes stem in some forms:

• sentí
• sentiste
• sintió
• sentimos
• sentisteis
• sintieron

The accent mark shows the stress and also distinguishes the written form correctly.

• sentí = I felt
• without the accent, senti would be misspelled in standard Spanish

In the preterite of many -ir and -er verbs, the yo form ends in -í:

• viví = I lived
• comí = I ate
• sentí = I felt

Yes, it sounds completely natural in Spain Spanish.

A native speaker in Spain would readily understand and use:

• Después de la conversación, me sentí más tranquilo.

Other natural alternatives might be:

• Después de hablar, me sentí más tranquilo.
• Tras la conversación, me quedé más tranquilo.

That last one, me quedé más tranquilo, is also very common in Spain when something reassures you.

Both can be translated as I felt calmer, but they are not exactly identical.

• me sentí más tranquilo focuses on the feeling itself
• me quedé más tranquilo often suggests I was reassured or I ended up feeling calmer after something happened

So if the conversation removed a worry, Spanish speakers in Spain might very naturally say:

• Después de la conversación, me quedé más tranquilo.

But your original sentence is still perfectly correct and natural.