По прилёте мы сразу написали родителям, что долетели спокойно.

It means upon arrival or after landing.

In this sentence, по прилёте sets the time frame for the main action: first we arrived, and then we immediately wrote to our parents.

It is a fairly compact, slightly formal way to say this. In more everyday speech, Russians might also say:

• после прилёта
• когда мы прилетели

Both are possible, but they are a little different in style.

• по прилёте = more formal, compact, slightly bookish
• после прилёта = more neutral and common in everyday speech

So this sentence sounds perfectly natural, but a bit more polished than casual conversation.

It is the prepositional singular of прилёт.

• nominative: прилёт
• genitive: прилёта
• prepositional: прилёте

In this special time expression, по means something like after/upon, and it is used with this form: по прилёте.

Because the verb писать / написать takes the dative case for the person you write to.

So:

• написать кому? = to write to whom?
• родителям = to the parents

This is plural dative of родители.

Compare:

• Я написал другу. = I wrote to a friend.
• Мы написали родителям. = We wrote to our parents.

Because написали is perfective, and here the speaker is talking about a completed action: the message was sent/written.

• писали would mean were writing / used to write / wrote in an imperfective sense
• написали means wrote with a clear result

Since the sentence describes a finished event, написали is the natural choice.

This is a very good question, because the two verbs are close in meaning.

• прилететь = to arrive by plane / to fly in
• долететь = to make it all the way by plane, to reach the destination by flying

In this sentence, долетели спокойно suggests we made it there without problems, we got there safely / smoothly.

So долетели emphasizes the successful completion of the trip, not just the fact of arrival.

Literally, yes: спокойно means calmly or peacefully.

But in this context, it is more natural in English as:

• safely
• without incident
• without any problems
• smoothly

So что долетели спокойно means that the flight went fine and nothing bad happened. It does not only describe the passengers' emotions.

Because что introduces a subordinate clause.

Main clause:

• мы сразу написали родителям

Subordinate clause:

• что долетели спокойно

Russian normally separates this kind of that-clause with a comma.

Russian often relies on context and aspect, not a special past perfect form like English had written / had arrived.

Here the order is clear:

1. По прилёте already tells us the arrival happened first.
2. Then мы сразу написали родителям happened after that.
3. The clause что долетели спокойно reports the earlier completed result.

So even though both verbs are past tense, the meaning is unambiguous.

Russian word order is flexible, but the chosen order sounds very natural.

• По прилёте comes first to set the scene: upon arrival
• мы сразу написали родителям gives the main action
• что долетели спокойно gives the content of what was written

Putting сразу before написали emphasizes immediately.

A different order is possible, but this version is smooth and standard.

Not always.

Russian often drops subject pronouns when they are clear from the verb form or the context. So написали already tells you the subject is we or they, depending on context.

But мы is included here because it makes the sentence clearer and more explicit. It can also add a slight sense of contrast or emphasis.

So:

• По прилёте сразу написали родителям... = possible if context is already clear
• По прилёте мы сразу написали родителям... = clearer and more complete on its own

People will definitely understand it, but in everyday speech many speakers would more often say:

• после прилёта
• когда мы прилетели
• как только прилетели

So по прилёте is natural Russian, just a little more formal or written in tone than the most conversational alternative.