Learn Hardcore Chinese: tā bǎ wǒ de diànnǎo jièzǒu le. - He borrowed my computer and took it away.

把 lets you front the object and highlight how it was affected. Pattern: Subject + 把 + definite object + Verb (often with a result/complement/aspect).
Here, 他把我的电脑借走了 emphasizes the outcome: your computer ended up gone from here.
Without 把, you can still say it, but the focus is less on “disposing of” the object.

Can I say this without 把?

Yes:

他借走了我的电脑。 (Natural; same meaning and emphasis on “took it away.”)
他借了我的电脑。 (Just “borrowed my computer,” doesn’t highlight the “away” result as strongly.) Using 把 is a stylistic choice to spotlight the affected object and the result.

What does 走 add to 借? How is it different from 借, 借去, 借来, 借到?

借: to borrow/lend (neutral).
借走: borrow and take it away from here; emphasizes removal.
借去: similar to 借走, directionally “away”; a bit more formal/regional.
借来: borrow and bring here. Example: 他把你的电脑借来了 (“brought it here”).
借到: emphasizes successful obtaining. Example: 我终于借到了那本书. Rule of thumb: 走 = away, 来 = toward the speaker, 到 = successfully obtained.

Is 了 here the perfective aspect 了? Could/should there be another 了 at the end?

In 借走了, 了 is the perfective marker (completed action).
You don’t add another 了 at the very end; this one already sits at sentence end and does the job.
Contrast:
- Affirmation of a finished event: 他把我的电脑借走了。
- Intention/command (no perfective): 他要把我的电脑借走。/ 别把我的电脑借走！

How do I negate or ask questions with this sentence?

Negative (use 没/没有 and drop 了): 他没(有)把我的电脑借走。
Yes–no (with 吗): 他把我的电脑借走了吗？
A–not–A: 他把我的电脑借走了没有/没？ or 他借没借走我的电脑？

What’s the passive version?

我的电脑被他借走了。 Focus shifts to the computer as the affected party.
Colloquial passive with 给 is also heard: 我的电脑给他借走了。 (Informal.)

Is 借 ambiguous between “borrow” and “lend”? How do I avoid confusion?

Yes, 借 by itself can be ambiguous; disambiguate with patterns:

A 借给 B 东西 = A lends something to B. Example: 他把他的电脑借给了我。
A 向/跟 B 借东西 = A borrows something from B. Example: 他向我借了电脑。 Your sentence with 借走 and the object 我的电脑 naturally reads as “he borrowed it (from me) and took it away.”

Could I say 他把我的电脑借了 (without 走)?

It’s grammatical but feels incomplete or less natural because 把-sentences typically want a clear result, direction, or complement. More natural options:

他借了我的电脑。 (no 把)
他把我的电脑借给别人了。 (gives a clear result/recipient)
他把我的电脑借走了。 (result: taken away)

Why is 的 used after 我? Can I drop it and say 我电脑?

的 marks possession: 我的电脑 = “my computer.”
Dropping 的 is common with close kinship/body parts (我妈, 我手) or set phrases. For ordinary objects like 电脑, 我的电脑 is standard. 我电脑 sounds dialectal or very casual; avoid it in standard Mandarin.

Do I need a measure word for 电脑? Which one?

When just referring to “my computer,” no measure word is needed: 我的电脑.
When counting/specifying: use 台. Examples:
- 我的一台电脑 (“one of my computers”)
- 他把我的一台电脑借走了。

Where do time/place words go with a 把 sentence?

Time usually goes before the subject or after it but before 把:
- 昨天他把我的电脑借走了。 / 他昨天把我的电脑借走了。
Place phrases often go before 把 or as prepositional phrases:
- 他在办公室把我的电脑借走了。
- 他把我的电脑从我这里借走了。 Avoid: 他把我的电脑昨天借走了 (sounds awkward).

How does this differ from 他借走了我的电脑 in nuance?

他把我的电脑借走了 puts 我的电脑 up front and highlights its fate (classic “disposal” focus).
他借走了我的电脑 is a neutral SVO order; focus is more on the action itself. Both are natural; the 把 version sounds a bit more object/result-focused.

Is 借走 the most natural choice? How about 拿走 or 带走?

借走 is natural when the means is “borrowing.”
拿走 = “take away (by picking it up),” doesn’t imply permission; could imply he just took it.
带走 = “take along (carry away),” often used when leaving with the item. If you want to stress it was a loan, 借走 is best.

Any pronunciation tips (tones, sandhi, neutral tones)?

把 bǎ (3rd) + 我 wǒ (3rd): 3–3 becomes 2–3 in speech, so pronounce it like bá wǒ.
的 de and aspect 了 le are neutral tone here.
电脑 diànnǎo is 4–3; make sure the third tone on nǎo dips appropriately unless followed by another 3rd tone.

How would I politely say “Could I borrow your computer?” and “Could you lend me your computer?”

Borrow: 我可以借一下你的电脑吗？ / 能借用一下你的电脑吗？ (借用 is a bit more formal/polite)
Lend: 你可以把你的电脑借给我吗？ / 能把电脑借给我一下吗？