Mi malfermas mian kajeron kaj skribas sur la papero per plumo.

Because kajeron is the direct object of malfermas (open), so it takes the accusative ending -n.
Any adjective or possessive word that goes with that noun must match it, so:

• mia kajero = my notebook (subject form)
• mian kajeron = my notebook (object form)

In Esperanto, agreement is very regular: if the noun has -n, the modifier does too.

The -n marks the direct object: the thing directly affected by the verb.

Here:

• Mi malfermas mian kajeron = I open my notebook

The notebook is the thing being opened, so kajero becomes kajeron.

A useful beginner rule is:

• subject = no -n
• direct object = -n

Because sur can express either:

• location: on, on top of
• movement toward a place: onto

Here, skribas sur la papero means writes on the paper, describing where the writing happens. That is location, so there is no -n.

Compare:

• Mi skribas sur la papero. = I write on the paper.
• Mi metas la libron sur la tablon. = I put the book onto the table.

In the second sentence, there is motion toward the surface, so tablon gets -n.

Per means by means of, using, or with the help of. It shows the instrument or tool used to do something.

So:

• per plumo = with a pen / using a pen

This is different from English with, which can mean several things. Esperanto often separates those meanings clearly:

• per plumo = using a pen
• kun amiko = with a friend

So per is the natural choice for a writing tool.

Because the sentence is talking about the tool in a general sense: with a pen, not necessarily with the specific pen.

So:

• per plumo = with a pen
• per la plumo = with the pen

Both are possible, but they mean slightly different things. The version without la is often used when the exact identity of the object is not important.

Yes. Mal- is a very common Esperanto prefix meaning the opposite of an idea.

• fermi = to close
• malfermi = to open

So malfermas literally comes from the opposite of close.

This is one of the most useful word-building patterns in Esperanto. For example:

• bona = good

• malbona = bad

• granda = big
• malgranda = small

The ending -as marks the present tense.

So:

• malfermas = open / am opening
• skribas = write / am writing

Esperanto does not usually force a distinction like English does between I open and I am opening. The context tells you which is meant.

Because the same subject continues across both verbs.

• Mi malfermas mian kajeron kaj skribas...

This means I open my notebook and write...
Esperanto, like English, often omits the repeated subject when it is the same.

You could say Mi malfermas mian kajeron kaj mi skribas..., but it would usually sound unnecessary unless you wanted special emphasis.

Because kaj is the normal Esperanto coordinating conjunction meaning and.

Here it connects two actions with the same subject:

• malfermas = open
• skribas = write

So:

• Mi malfermas mian kajeron kaj skribas...
  = I open my notebook and write...

Usually yes in basic usage, but vocabulary never matches perfectly across languages.

Kajero generally means a notebook, exercise book, or copybook: a bound set of pages for writing.

So for a learner, notebook is the right translation here, but it is good to remember that Esperanto words often cover a slightly different range than one exact English word.

Yes, Esperanto word order is fairly flexible because endings show the grammar.

The neutral order here is very natural:

• Mi malfermas mian kajeron kaj skribas sur la papero per plumo.

But some parts could be moved for emphasis, for example:

• Per plumo mi skribas sur la papero.
• Sur la papero mi skribas per plumo.

Even so, beginners should usually stick to the most straightforward order until they are comfortable with the language.

No, not really. Sur la papero means on the paper. It refers to the surface of the paper.

If you wanted in the notebook, you would normally say something like:

• en la kajero = in the notebook

So the sentence gives two separate objects/places:

• mian kajeron = the notebook I open
• sur la papero = the paper on which I write

It can depend on context. In this sentence, la papero most naturally suggests a particular piece of paper or the paper being written on.

Esperanto often uses the singular where English might also say paper in an uncountable sense, but here the image is probably a sheet or specific writing surface.

So a learner can safely understand:

• sur la papero = on the paper

without worrying too much about whether English would say paper or a sheet of paper in another context.