Нам легче прощать друг друга после спокойного разговора.

Because this sentence uses an impersonal pattern:

кому-то легче + infinitive = it is easier for someone to do something

So нам is the dative case of мы, meaning to us / for us.

A very literal breakdown is:

Нам легче прощать друг друга...
= For us, it is easier to forgive each other...

If you used мы, that would suggest we as the grammatical subject, which is not how this structure works in Russian.

Легче means easier. It is the comparative form related to легко (easily) and лёгкий (light, easy).

In this kind of sentence, легче functions as a predicative word: it describes how easy or difficult an action is.

Common similar patterns:

• Мне трудно понять. = It is hard for me to understand.
• Ему легко говорить. = It is easy for him to speak.
• Нам легче прощать. = It is easier for us to forgive.

So here легче is not modifying a noun. It is part of the whole idea it is easier to...

In present-tense Russian, есть is usually omitted.

So Russian often says:

• Мне трудно.
• Нам легче.
• Ей интересно.

without any separate word for is.

So:

Нам легче прощать друг друга...

naturally means:

It is easier for us to forgive each other...

There is no missing word from a Russian point of view; the sentence is complete as it stands.

Because after words like легче, Russian often uses the pattern:

кому + легче/трудно/можно/нужно + infinitive

So прощать is the action that is being described as easier.

Compare:

• Мне легко читать. = It is easy for me to read.
• Им трудно работать. = It is hard for them to work.
• Нам легче прощать. = It is easier for us to forgive.

A conjugated verb such as прощаем would create a different structure and a different meaning.

This is an aspect question.

• прощать = imperfective
• простить = perfective

Here прощать sounds natural because the sentence talks about forgiveness in a general sense or as a process/ability:

After a calm conversation, forgiving each other is easier for us.

Using простить would shift the focus more toward one completed act of forgiveness:

Нам легче простить друг друга после спокойного разговора.
= After a calm conversation, it is easier for us to forgive each other completely / to manage to forgive each other.

So both can be possible in some contexts, but прощать is better for a general statement about what becomes easier.

Друг друга means each other.

It is a fixed reciprocal expression in Russian. In this sentence, it is the object of прощать, so it means:

forgive each other

You will see it in different case forms depending on grammar:

• любить друг друга = to love each other
• помогать друг другу = to help each other
• говорить друг с другом = to talk with each other
• думать друг о друге = to think about each other

In your sentence, друг друга is in the form required as the direct object of прощать.

Because the preposition после always requires the genitive case.

So:

• разговор → разговора (genitive singular)
• спокойный → спокойного (genitive singular masculine, agreeing with разговора)

That is why you get:

после спокойного разговора
= after a calm conversation

This is a very common rule:

• после урока = after the lesson
• после работы = after work
• после длинного дня = after a long day

Because it is agreeing with разговора in:

• gender: masculine
• number: singular
• case: genitive

The dictionary form is спокойный разговор.

After после, both words go into the genitive:

• спокойный → спокойного
• разговор → разговора

So the adjective changes because Russian adjectives must match the noun they describe.

Yes. Russian word order is flexible.

The sentence

Нам легче прощать друг друга после спокойного разговора.

is natural and neutral.

But other orders are also possible, with slightly different emphasis:

• После спокойного разговора нам легче прощать друг друга.
  Emphasizes after a calm conversation.

• Друг друга нам легче прощать после спокойного разговора.
  Puts extra focus on each other.

The original version is a good standard order for learners.

Yes. It does not have to mean only two people.

Like English each other, it can refer to:

• two people
• several people in a group

So Нам легче прощать друг друга can mean:

• it is easier for the two of us to forgive each other
• it is easier for us, as a group, to forgive one another

The exact meaning depends on context.

Not exactly.

Нам легче прощать друг друга... means:
It is easier for us to forgive each other...

This focuses on ease/difficulty.

Мы легче прощаем друг друга... is much less natural in this context and sounds more like:
We forgive each other more easily...

That is closer in meaning, but the Russian sentence with нам легче + infinitive is the standard and more idiomatic way to express the idea.