Ŝi bezonas pli da tempo por sia maleolo kaj kokso.

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

Here the subject is Ŝi, so sia maleolo kaj kokso means her own ankle and hip.

If you used ŝia instead, it would normally mean another woman's ankle and hip, not the subject's.

Pli means more, and da is used after words of quantity or amount.

So:

• pli da tempo = more time
• literally, something like more of time

Esperanto normally uses da after amount words such as:

• multe da akvo = a lot of water
• iom da mono = some money
• pli da tempo = more time

Using just pli tempo would not be the normal standard form here.

Because in a da-phrase, the noun after da normally stays in its basic form.

So you say:

• pli da tempo

not

• pli da tempon

The whole expression pli da tempo functions as the object of bezonas, but the noun after da does not take the accusative ending.

Compare:

• Ŝi bezonas tempon = She needs time.
• Ŝi bezonas pli da tempo = She needs more time.

Por usually means for in the sense of for the benefit of, intended for, or for the purpose of.

Here, por sia maleolo kaj kokso means the extra time is for her ankle and hip—in context, probably meaning for them to recover/heal.

So the sentence is a natural Esperanto way to say that she needs more time because those body parts are not fully better yet.

Because they come after the preposition por.

In Esperanto, nouns after a preposition usually do not take the accusative -n. So:

• por sia maleolo kaj kokso = for her ankle and hip

They are not the direct object of bezonas. The direct object is pli da tempo.

Because the sentence is talking about one ankle and one hip.

That is completely normal, just like in English you might say her ankle and hip. If the meaning were both ankles or both hips, then Esperanto would use plurals:

• maleoloj
• koksoj

Yes. In Esperanto, one possessive can naturally apply to both nouns in a pair like this:

• sia maleolo kaj kokso

This means:

• her own ankle and hip

You could repeat it for extra clarity:

• sia maleolo kaj sia kokso

But that is not necessary here.

Because possessive words like mia, via, lia, ŝia, sia, nia, ilia already make the noun definite enough.

So Esperanto normally says:

• mia domo = my house
• ŝia mano = her hand
• sia kokso = her own hip

not usually:

• la mia domo
• la sia kokso

So sia maleolo kaj kokso is the normal form.

Usually, pli da tempo is the best choice for more time.

There is a difference:

• pli da tempo = a greater amount of time
• plia tempo = additional/further time

These can be close in meaning, but pli da tempo is the most natural match for ordinary English more time.

Because -as is the Esperanto ending for the present tense.

So:

• mi bezonas = I need
• ŝi bezonas = she needs
• ili bezonas = they need

The verb ending does not change with the person. Esperanto verbs are much simpler than English in that way.

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

The original order is the most neutral:

• Ŝi bezonas pli da tempo por sia maleolo kaj kokso.

But you could also say:

• Por sia maleolo kaj kokso ŝi bezonas pli da tempo.

That puts more emphasis on for her ankle and hip.

Both are grammatical; the original version is just the most straightforward.