Mi prunteprenas la novan eldonon por du semajnoj.

It is a compound word:

• prunte = on loan
• preni = to take

So pruntepreni literally means to take on loan, which is the normal Esperanto way to say to borrow.

The ending -as shows present tense, so prunteprenas means borrow / am borrowing.

Because preni only means to take. It does not by itself include the idea of borrowing.

pruntepreni is more specific: it clearly means that you take something temporarily and will give it back. Esperanto often uses compounds like this to make the meaning precise.

Because la novan eldonon is the direct object of the verb.

In Esperanto, a direct object usually takes the accusative ending -n. Since eldono is the noun being borrowed, it becomes eldonon.

The adjective nova must agree with the noun, so it also takes -n and becomes novan.

So:

• nova eldono = a new edition
• novan eldonon = a new edition as a direct object

Adjectives in Esperanto agree with the nouns they describe in both number and case.

So if the noun is:

• plural, the adjective becomes plural too
• accusative, the adjective becomes accusative too

Here, eldonon is singular accusative, so nova must match it and become novan.

That agreement is one of the regular patterns of Esperanto grammar.

la means the. It shows that the speaker means a specific edition, not just any edition.

So:

• nova eldono = a new edition
• la nova eldono = the new edition

Also, Esperanto has no separate word for a/an. If something is indefinite, you usually just leave out the article.

por du semajnoj means for two weeks.

Here por shows the intended period or arrangement: the speaker is borrowing the edition with a loan period of two weeks.

That fits this kind of context very well, especially for libraries or temporary loans.

Because it comes after the preposition por.

After a preposition, nouns normally do not take the direct-object ending -n. So you get:

• por du semajnoj = for two weeks

The -j is there only because du semajnoj is plural.

You could, but it is not exactly the same in feel.

• por du semajnoj = for a two-week loan period; intended duration
• dum du semajnoj = during two weeks; over the course of two weeks

With borrowing, por du semajnoj is usually the more natural choice, because you are stating how long the item is being borrowed for.

In Esperanto, the present tense often covers what English expresses as either:

• I borrow
• I am borrowing

So Mi prunteprenas... can naturally mean I am borrowing...

If you wanted to make it clearly future, you would use -os:

• Mi prunteprenos la novan eldonon... = I will borrow the new edition...

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

For example, this is also possible:

La novan eldonon mi prunteprenas por du semajnoj.

That is still grammatical because -n shows that la novan eldonon is the object.

However, Mi prunteprenas la novan eldonon por du semajnoj is the most neutral and straightforward order.

eldono usually means edition, issue, or published version.

In this sentence, the most likely meaning is edition, especially if the thing being borrowed is a book or similar publication.

So la novan eldonon means the newer edition of that work, not just any copy.

The usual opposite of pruntepreni is pruntedoni.

• pruntepreni = borrow
• pruntedoni = lend

So a sentence with lend might be:

Mi pruntedonas la novan eldonon al li por du semajnoj.

That means I lend him the new edition for two weeks.

Notice the receiver is introduced with al.