Mia fratino preferas skribi per krajono en sia kajero, sed mi uzas plumon.

Yes. -in- is the feminine suffix in Esperanto.

• frato = brother
• fratino = sister

So mia fratino literally breaks down as my sister.

Because the Esperanto infinitive already includes that meaning.

• skribi = to write
• preferas skribi = prefers to write

In Esperanto, infinitives end in -i, so you do not add a separate word like English to.

Per means by means of, using, or with in the sense of a tool or instrument.

So:

• skribi per krajono = to write with a pencil
• uzi plumon = to use a pen

A useful contrast is:

• per = using something as a means
• kun = with, together with

So here per is correct because the pencil is the instrument used for writing.

Because nouns after a preposition usually do not take the accusative -n.

Here krajono comes after per, so it stays as krajono.

The -n ending is mainly used for:

• direct objects
• direction in some expressions

Since krajono is not the direct object of the sentence, there is no -n here.

Because sia is the reflexive possessive adjective. It refers back to the subject of the same clause.

In the first clause, the subject is mia fratino, so:

• en sia kajero = in her own notebook

If you said ŝia kajero, it would usually mean in her notebook, where her could be someone else, not necessarily the sister who is the subject.

So:

• sia = the subject’s own
• ŝia = her, possibly someone else’s

Because en here shows location, not direction.

• en sia kajero = in her notebook

When a preposition shows simple location, the noun normally stays without -n.

Esperanto can use -n after a preposition to show movement toward something, but that is not happening here. The sentence is about where she writes, not motion into the notebook.

Because plumon is the direct object of uzas.

• mi uzas plumon = I use a pen

The thing being used is the direct object, so it takes -n.

That is why:

• krajono has no -n after per
• plumon has -n because it is the object of uzas

Esperanto has no indefinite article.

So English a pencil is simply krajono, and a pen is plumon here.

Esperanto does have a definite article, la, for the, but it is only used when needed. In this sentence, the nouns are understood well enough without la, so leaving it out is natural.

Yes, Esperanto word order is fairly flexible, although the usual order is similar to English.

This sentence uses a normal pattern:

• Mia fratino preferas...
• sed mi uzas...

Because Esperanto marks grammar clearly with endings like -n, you can sometimes move parts around for emphasis. But the version given is the most straightforward and natural for a learner.

Both are natural, but they focus on slightly different things.

• preferas skribi per krajono emphasizes the preferred way of writing
• uzas plumon simply states what the speaker uses

So the sentence contrasts:

• what the sister prefers to write with
• what the speaker uses instead

You could make the two halves more parallel in other ways, but the original sentence sounds normal and idiomatic.