Ich trage den Termin in meinen Kalender ein.

Because the verb here is eintragen, which is a separable verb.

• Infinitive: eintragen
• Main clause, present tense: Ich trage ... ein.

So the verb splits:

• trage goes to the usual verb position
• ein goes to the end

That is very common with separable verbs in German:

• Ich rufe dich an. = I call you.
• Er kauft Brot ein. = He shops for bread / buys groceries.
• Ich trage den Termin ein. = I enter the appointment.

In some other structures, the verb does not split:

• Ich will den Termin eintragen.
• ..., weil ich den Termin eintrage.

Here eintragen means to enter something into a calendar, list, form, or system.

So Ich trage den Termin in meinen Kalender ein means something like:

• I enter the appointment in my calendar.
• I put the appointment into my calendar.
• I write the appointment into my calendar.

It is more specific than just schreiben (to write).
eintragen suggests that you are recording something in the proper place, not just writing randomly.

Compare:

• Ich schreibe den Termin auf. = I write the appointment down.
• Ich notiere den Termin. = I note down the appointment.
• Ich trage den Termin in meinen Kalender ein. = I enter the appointment into my calendar.

Because den Termin is the direct object of the verb, so it is in the accusative case.

The noun Termin is masculine:

• Nominative: der Termin
• Accusative: den Termin

In this sentence, I am doing something to the appointment, so Termin is the thing being entered.

Compare:

• Der Termin ist morgen.
  Here der Termin is the subject.
• Ich trage den Termin ein.
  Here den Termin is the object.

Because Kalender is masculine, and after in here the phrase is in the accusative.

The possessive mein changes like an article:

• Nominative masculine: mein Kalender
• Accusative masculine: meinen Kalender

So:

• mein Kalender = my calendar
• in meinen Kalender = into my calendar

It is not meinem Kalender here, because meinem would be dative.

In is a two-way preposition in German. That means it can take either:

• dative for location
• accusative for direction or movement into something

Here the idea is figuratively putting/entering the appointment into the calendar, so German uses the accusative:

• in meinen Kalender = into my calendar

Compare:

• Der Termin steht in meinem Kalender.
  The appointment is in my calendar.
  → location, so dative: in meinem Kalender

• Ich trage den Termin in meinen Kalender ein.
  I enter the appointment into my calendar.
  → direction/change, so accusative: in meinen Kalender

Even though nothing is physically moving, German still treats this as a kind of figurative movement.

No. Termin is a false friend.

In this sentence, Termin usually means:

• appointment
• scheduled meeting
• time slot

Examples:

• Ich habe morgen einen Termin beim Arzt. = I have a doctor’s appointment tomorrow.
• Wir müssen einen Termin vereinbaren. = We need to arrange an appointment.

It does not usually mean English term in the sense of a word, school semester, or condition.

So in this sentence, den Termin is most naturally the appointment or the scheduled event.

Yes, it is natural.

A German speaker would understand it immediately as I’m entering the appointment into my calendar.

You might also hear close alternatives, for example:

• Ich trage den Termin in den Kalender ein.
• Ich trage mir den Termin in den Kalender ein.

The version with mir adds the idea for myself:

• Ich trage mir den Termin in den Kalender ein.
  = I enter the appointment into my calendar for myself / I make a note of it in my calendar.

Your original sentence with meinen Kalender is completely fine and clear.

Yes. German word order is flexible, but the finite verb in a main clause still stays in second position, and the separable prefix ein still goes to the end.

For example:

• Ich trage den Termin in meinen Kalender ein.
• Den Termin trage ich in meinen Kalender ein.
• In meinen Kalender trage ich den Termin ein.

All of these are possible. What changes is the emphasis:

• Ich at the beginning: neutral
• Den Termin at the beginning: emphasis on the appointment
• In meinen Kalender at the beginning: emphasis on where it is being entered

Because all nouns are capitalized in German.

So here:

• Termin is a noun
• Kalender is a noun

That is why both start with capital letters.

This is one of the most noticeable spelling differences between English and German.

Because eintragen is separable, its form changes depending on the structure.

Present:

• Ich trage den Termin in meinen Kalender ein.

Perfect:

• Ich habe den Termin in meinen Kalender eingetragen.

With a modal verb:

• Ich will den Termin in meinen Kalender eintragen.

Subordinate clause:

• ..., weil ich den Termin in meinen Kalender eintrage.

So the key pattern is:

• main clause, simple tense → split: trage ... ein
• infinitive / subordinate clause / participle → usually together: eintragen, eintrage, eingetragen

Sometimes, yes, but the meaning is slightly different.

• aufschreiben = write down
• eintragen = enter into a specific place such as a calendar, form, list, or register

So:

• Ich schreibe den Termin auf.
  I write the appointment down.

• Ich trage den Termin in meinen Kalender ein.
  I enter the appointment in my calendar.

If you want to emphasize that the appointment is being added to a calendar, eintragen is the better choice.