Мы понимаем друг друга лучше, когда говорим спокойно.

Друг друга means each other or one another.

So:

• Мы понимаем друг друга = We understand each other

Even though друг by itself can mean friend, in this expression друг друга is a fixed reciprocal phrase. You should learn it as a unit.

Because понимать usually takes an object: you understand someone or something.

Here, the object is друг друга = each other.

• Мы понимаем = We understand
  This is grammatically possible, but incomplete unless the context already makes clear what or whom we understand.
• Мы понимаем друг друга = We understand each other

So друг друга completes the idea.

Here друг друга is the direct object of понимаем, so it is in the accusative pattern.

However, with animate masculine forms in Russian, the accusative often looks like the genitive. That is why you see друга.

In practice, learners usually memorize this as the standard expression:

• понимать друг друга = to understand each other

Other verbs can require other forms:

• помогать друг другу = to help each other
• довольны друг другом = pleased with each other

So the form changes depending on the grammar of the sentence.

Лучше means better.

It is the comparative form of хорошо in adverb use, so here it means:

• понимаем лучше = understand better

In this sentence, it tells us that the understanding becomes better under a certain condition:

• Мы понимаем друг друга лучше, когда...
  = We understand each other better when...

So лучше modifies the verb понимаем.

Because когда говорим спокойно is a subordinate clause.

Russian normally uses a comma before words like когда, если, потому что, что, etc. when they introduce a subordinate clause.

So:

• Мы понимаем друг друга лучше, когда говорим спокойно.

Literally, the structure is:

• We understand each other better, when we speak calmly.

English usually does not need that comma here, but Russian does.

Because Russian often omits subject pronouns when the verb ending already shows who is doing the action.

• говорим already means we speak / we are speaking

So когда говорим спокойно naturally means:

• when we speak calmly

You could say когда мы говорим спокойно, but that would be more explicit or slightly more emphatic. The version without мы sounds very natural.

Because спокойно is an adverb, and here Russian needs an adverb to describe how we speak.

• говорим спокойно = speak calmly

Compare:

• спокойный человек = a calm person
  Here спокойный is an adjective describing a noun.
• говорить спокойно = to speak calmly
  Here спокойно is an adverb describing a verb.

English does the same thing:

• a calm person
• to speak calmly

Not exactly.

Спокойно means calmly, peacefully, without agitation, in a relaxed way.

If you want quietly in the sense of not loudly, Russian more often uses тихо.

So:

• говорить спокойно = speak calmly
• говорить тихо = speak quietly / softly

Sometimes the ideas overlap in real life, but they are not the same word.

Because the sentence expresses a general truth or repeated situation:

• We understand each other better when we speak calmly

This is not about one completed event. It is about what generally happens.

So Russian uses imperfective verbs:

• понимаем from понимать
• говорим from говорить

If you used perfective forms, the meaning would change and sound more like a single completed future event, not a general statement.

Yes. That is a very natural translation.

Some close English versions are:

• We understand each other better when we speak calmly.
• We understand one another better when we talk calmly.
• We understand each other better when we speak in a calm way.

The Russian sentence itself is neutral and natural.

Yes, you could say:

• Мы понимаем друг друга лучше, когда разговариваем спокойно.

That is also natural, but there is a slight nuance:

• говорить = to speak
• разговаривать = to converse / talk with each other

Since the sentence is about mutual understanding, разговариваем can sound a little more explicitly two-way. But говорим is completely fine and idiomatic here.

No, Russian word order is flexible, although some versions sound more natural than others.

The original sentence is very natural:

• Мы понимаем друг друга лучше, когда говорим спокойно.

You could also hear:

• Мы лучше понимаем друг друга, когда говорим спокойно.

That version puts a bit more emphasis on better.

Russian word order often changes emphasis rather than basic meaning. For learners, the original order is an excellent model to follow.