tomodati to hisasiburi ni tuuwasita ato, raisyuu no yotei wo tetyou ni kaita.

Here, と means with and marks the person you did the action together with.

• 友達と通話した = I had a call with a friend

It is different from:

• 友達に = to a friend / marks the target of an action
• 友達が = marks friend as the subject

With communication verbs, both 友達と話した and 友達に話した can exist, but they mean slightly different things:

• 友達と話した = talked with a friend
• 友達に話した = talked to a friend

Since this sentence is about a mutual phone conversation, と fits well.

久しぶり means something like after a long time or for the first time in a while.
When used adverbially before a verb, it often takes に:

• 久しぶりに会った = met after a long time
• 久しぶりに通話した = talked on the phone for the first time in a while

So に helps turn 久しぶり into an adverb-like expression modifying the verb.

A useful comparison:

• 久しぶり！ = Long time no see!
• 久しぶりに電話した = I called for the first time in a while

通話する specifically means to talk on the phone / have a phone conversation.
話す just means to speak / talk, and does not by itself tell you it was a phone call.

So:

• 友達と話した = talked with a friend
• 友達と通話した = had a phone call with a friend

Because the sentence wants to be specific about the method of communication, 通話した is used.

あと means after. When it follows a verb in plain past form, it means after doing ...

• 通話したあと = after having a phone call
• 食べたあと = after eating
• 帰ったあと = after going home

So the structure is:

• [plain past verb] + あと
• 通話した + あと → after I talked on the phone

This phrase sets up the time relationship: first the call happened, then the writing happened.

Because 通話したあと literally means after having done the call.

With あと, Japanese often uses:

• verb past plain + あと = after doing something

Examples:

• 宿題をしたあと、寝た。 = After doing homework, I slept.
• ご飯を食べたあと、散歩した。 = After eating, I took a walk.

The past form here does not necessarily mean the whole sentence is “past inside past” in a complicated way. It simply marks the action as completed before the next one.

来週 = next week
予定 = plans / schedule

の connects the two nouns, so:

• 来週の予定 = next week’s plans / the schedule for next week

This is the very common noun-linking use of の.

More examples:

• 明日の天気 = tomorrow’s weather
• 日本の文化 = Japanese culture
• 学校の先生 = school teacher / teacher at school

So 来週の予定 is just a noun phrase meaning the plans belonging to next week.

Because 予定 is the direct object of 書いた.

• 予定を書いた = wrote the plans

The sentence is saying what was written, and を marks that thing.

Structure:

• 来週の予定 = what was written
• を = object marker
• 手帳に書いた = wrote in a planner/notebook

So 来週の予定を手帳に書いた = wrote next week’s plans in a planner.

Here に marks the place where the writing is put.

• 手帳に書いた = wrote it in a planner
• ノートに書いた = wrote it in a notebook
• 紙に書いた = wrote it on paper

With 書く, に often marks the surface, medium, or location where something is written.

Compare:

• 手帳を書く is not correct for this meaning
• 手帳に書く = write in the planner
• 手帳を書く would sound like write a planner, which is not the intended idea

Because the whole sentence is describing completed actions in the past.

Sequence:

1. 友達と久しぶりに通話した = I talked on the phone with a friend after a long time
2. あと、来週の予定を手帳に書いた = after that, I wrote next week’s plans in my planner

Both actions are presented as things that already happened.

Also note:

• The first した is inside the あと phrase: after I had the call
• The final 書いた is the main verb of the sentence

Japanese often omits subjects when they are clear from context.

So even though English would usually say:

• I talked with a friend...
• I wrote next week’s plans...

Japanese often leaves 私 out unless it is needed for emphasis or contrast.

A natural full version could be:

• 私は友達と久しぶりに通話したあと、来週の予定を手帳に書いた。

But in normal conversation or writing, that 私は is often unnecessary.

Not exactly in the same structure.

• 通話したあと = after having a phone call
• 後で = later / afterwards

So you could say:

• 友達と久しぶりに通話した。後で、来週の予定を手帳に書いた。

But that sounds more like two separate statements:
I had a phone call with a friend. Later, I wrote next week’s plans in my planner.

The original 通話したあと、... more tightly connects the two actions as a sequence.

Yes, somewhat. Japanese word order is more flexible than English, as long as the particles make the roles clear.

Original:

• 友達と久しぶりに通話したあと、来週の予定を手帳に書いた。

Possible variation:

• 来週の予定を、友達と久しぶりに通話したあと、手帳に書いた。

This is still understandable because:

• と marks friend as the companion
• を marks plans as the object
• に marks planner as the place

However, the original order is natural and easy to follow: first the earlier action, then the main action.

Not quite.

• 手帳 usually means a personal planner, agenda, or datebook
• ノート means a notebook
• メモ帳 means a memo pad / small notepad

So 手帳に書いた suggests writing plans into a schedule book or planner, which matches 来週の予定 very naturally.

That is why 手帳 is a good word choice here: it suggests organizing upcoming plans, not just writing random notes.