Mi skribas en mia kalendaro, ke merkrede ni vizitos la bibliotekon.

Ke means that. It introduces a subordinate clause:

• Mi skribas en mia kalendaro = I write/am writing in my calendar
• ke merkrede ni vizitos la bibliotekon = that on Wednesday we will visit the library

So ke connects the two parts, just like English that.

The comma marks the beginning of the subordinate clause introduced by ke. In Esperanto, commas are commonly used before clauses like this.

So:

• Mi skribas en mia kalendaro, ke...

is a normal and natural way to punctuate the sentence.

Merkredo is the noun Wednesday.
Merkrede is the adverbial form, meaning on Wednesday.

Esperanto often uses the -e ending for time expressions of this kind:

• lunde = on Monday
• marde = on Tuesday
• merkrede = on Wednesday

So merkrede is the natural way to say on Wednesday.

For days of the week, merkrede is the most common and elegant choice.

You may sometimes see other time expressions with je, but with weekdays Esperanto usually prefers the adverb form:

• merkrede = on Wednesday

So for a learner, merkrede is the form to remember and use.

Vizitos is the future tense of viziti = to visit.

• vizitas = visit / am visiting / do visit
• vizitos = will visit

Because the visit will happen on Wednesday, the future tense is used:

• ni vizitos la bibliotekon = we will visit the library

The -n ending marks the direct object. The library is the thing being visited, so it takes the accusative ending.

• ni vizitos la bibliotekon
• we will visit the library

In Esperanto, the direct object usually gets -n.

Compare:

• la biblioteko = the library
• la bibliotekon = the library, as the object of the verb

Because kalendaro is not the direct object here. It comes after the preposition en:

• en mia kalendaro = in my calendar

After a preposition like en, you normally do not add -n unless there is a special reason involving direction or motion. Here it just means location, so kalendaro stays without -n.

En means in. So:

• en mia kalendaro = in my calendar

This is the natural way to say that you are writing something inside your calendar/planner as an entry or note.

• mia = my
• kalendaro = calendar

So the phrase literally means in my calendar.

It can mean either, depending on context. Esperanto does not usually make the same present-tense distinction that English does.

So Mi skribas can mean:

• I write
• I am writing

In this sentence, English would most naturally say I am writing in my calendar..., but Esperanto simply uses the present tense skribas.

La is the definite article, meaning the.

• bibliotekon = a library / library, as object
• la bibliotekon = the library

The speaker probably has a specific library in mind, so la is used. Esperanto uses la much like English uses the.

Yes, Esperanto word order is fairly flexible, although some orders sound more neutral than others.

This sentence is very natural as written:

• Mi skribas en mia kalendaro, ke merkrede ni vizitos la bibliotekon.

But you could also move the time expression:

• Mi skribas en mia kalendaro, ke ni vizitos la bibliotekon merkrede.

Both are understandable. Putting merkrede earlier gives it a little more prominence.

Yes. Ni means we, including the speaker.

So:

• ni vizitos la bibliotekon = we will visit the library

If the speaker were not included, Esperanto would use some other wording, not ni.

Yes. It means to write something into a calendar or planner. In this sentence, the idea is that the speaker is making a note or entry.

So the whole sentence has the sense of:

• writing in a calendar/planner
• noting down that something will happen on Wednesday

That is a normal and natural use of skribi en mia kalendaro.