Mi jam skribis en la kalendaro, ke la dekan de decembro ni vizitos niajn geavojn.

Because the two actions happen at different times:

• skribis = the writing already happened
• vizitos = the visit will happen later

Esperanto chooses tense based on the actual time of each action. So after ke, you do not automatically shift the tense just because the main verb is past.

So the sentence means that earlier, I wrote down a plan about a future visit.

Jam means already or by now.

So Mi jam skribis... means that the speaker has already made that note in the calendar.

Its position is natural here: it comes before the verb it modifies. Esperanto often places jam right before the verb or the part of the sentence it most directly affects.

Because dates in Esperanto normally use an ordinal number, not a plain cardinal number.

• dek = ten
• deka = tenth

So:

• la deka de decembro = the tenth of December

In this sentence, it becomes la dekan de decembro because of the accusative, which is a separate issue.

A very common written form is also:

• la 10-an de decembro

Here the date is being used as a time expression, meaning on the tenth of December.

Esperanto often uses the accusative without a preposition to show the time when something happens. That is why the date takes -n.

So:

• la dekan de decembro = on the tenth of December

You can think of it as a shortened form of something like:

• la dekan tagon de decembro = the tenth day of December

Since the whole date phrase is functioning as a time expression, the accusative appears.

Because decembro is inside the phrase de decembro.

The word de is a preposition, and after a preposition, Esperanto normally does not add accusative -n just because the larger phrase is accusative.

So:

• la dekan = the main date element, carrying the accusative
• de decembro = of December, a prepositional phrase attached to it

That is why you get la dekan de decembro, not la dekan de decembron.

Yes, you can understand it as a shortened version of:

• la dekan tagon de decembro

Literally, that is the tenth day of December.

In normal Esperanto, the word tagon is usually omitted, just as English says the tenth of December rather than the tenth day of December in most contexts.

So learners should think of la dekan de decembro as a standard date expression, not as something unusual.

Ge- shows a group containing both sexes together.

So:

• avo = grandfather
• avino = grandmother
• geavoj = grandparents

In this sentence, geavojn is the accusative plural form because it is the direct object of vizitos.

So:

• niajn geavojn = our grandparents

This is a very common use of ge- in family words, such as:

• gepatroj = parents
• gefratoj = brothers and sisters / siblings

Because nia behaves like an adjective, and adjectives in Esperanto agree with the noun they describe.

Here:

• geavojn is plural: -j
• geavojn is also accusative: -n

So the possessive adjective must match:

• niajn geavojn

Breaking it down:

• nia = our
• niaj = our, plural
• niajn = our, plural accusative

This kind of agreement is a basic Esperanto pattern.

Because ke introduces a subordinate clause, and Esperanto normally separates that clause with a comma.

So the structure is:

• main clause: Mi jam skribis en la kalendaro
• subordinate clause: ke la dekan de decembro ni vizitos niajn geavojn

Using a comma before ke is standard Esperanto punctuation.

En la kalendaro is very natural when you mean in the calendar in the sense of entering something into it as a schedule, note, or appointment.

It focuses on the calendar as a system or record.

• en la kalendaro = in the calendar, as an entry
• sur la kalendaro = on the calendar, more physically on its surface

If you are talking about adding a date or plan to your calendar, en la kalendaro is perfectly normal.

Yes. Esperanto word order is fairly flexible, because endings show grammatical function.

For example, you could also say:

• Mi jam skribis en la kalendaro, ke ni vizitos niajn geavojn la dekan de decembro.

That has essentially the same meaning.

The original version puts the date early in the subordinate clause, which gives it a little more prominence. But both orders are natural.