После разговора мы молча идём домой.

Because после means after and it requires the genitive case.

The basic dictionary form is разговор.
After после, it changes to the genitive singular:

• разговор → nominative singular
• разговора → genitive singular

So:

• после разговора = after the conversation / after a conversation

Разговора is the genitive singular form of разговор, which means conversation, talk, or discussion.

In this sentence, it does not mean anything new by itself; it is simply the form required after после.

So the structure is:

• после
  • genitive
• после разговора = after the conversation

This is a very common Russian verbs-of-motion question.

• идти / идём is used for movement in one direction, especially a specific trip happening now.
• ходить / ходим is used for habitual, repeated, or multi-directional movement.

Here the sentence describes one specific movement home after the conversation, so идём is the natural choice.

Compare:

• Мы идём домой. = We are going home.
• Мы ходим домой пешком. = We go home on foot / We walk home regularly.

Yes. Russian present tense often covers both simple present and present continuous meanings.

So мы идём домой can mean:

• we go home
• we are going home

In this sentence, the most natural English translation is usually we are going home, because it sounds like an action happening now, after the conversation.

Молча means silently or without speaking.

It is an adverb, so it does not change for gender, number, or case.

It describes how we are going home:

• мы идём домой = we are going home
• мы молча идём домой = we are silently going home / we go home in silence

Because домой means homeward / to home, while дома means at home.

• домой = motion toward home
• дома = location at home

So:

• Мы идём домой. = We are going home.
• Мы дома. = We are at home.

This is a very important distinction in Russian.

Because домой already includes the meaning of movement toward home. It behaves like an adverb.

So Russian says:

• идти домой = to go home

not normally:

• идти в домой ✘

You may see в дом, but that means into the house/building, not simply home in the everyday sense.

It can be omitted if the subject is clear from context.

The ending -ём in идём already tells you the subject is we.

So both are possible:

• Мы молча идём домой.
• Молча идём домой.

Including мы can make the subject clearer or add slight emphasis, especially if you are contrasting we with someone else.

No. Russian word order is flexible, though some orders sound more neutral than others.

После разговора мы молча идём домой is a natural, neutral order.

You could also say:

• Мы после разговора молча идём домой.
• Мы идём домой молча.
• Домой мы идём молча.

The basic meaning stays similar, but the emphasis changes:

• earlier position often gives more prominence
• later position can sound more like added information

Russian has no articles, so there is no direct equivalent of a, an, or the.

That means разговор can mean:

• a conversation
• the conversation

depending on context.

In this sentence, English often uses the conversation because it sounds like a specific conversation already known to the speaker and listener.

Идём is pronounced roughly i-DYOM.

The letter ё is important because it always shows a stressed yo sound.

So:

• идём = stress on the second syllable
• the ё tells you the pronunciation clearly

In some Russian texts, people write е instead of ё, so you might see идем, but the correct pronunciation is still идём.

Usually, no.

После разговора is just a normal prepositional phrase at the start of the sentence, and in neutral Russian it is usually not separated by a comma:

• После разговора мы молча идём домой.

A comma might appear only in special stylistic cases, for example if the writer wants a strong pause, but that is not the normal default.