Learn Hardcore Korean: yakgugeseo yageul baedalhae jwosseo.

Korean often drops the subject when it’s clear from context. In this sentence, the most natural understood subject is the pharmacy staff or service. You can make it explicit:

약국이/약국에서 직원들이 약을 배달해 줬어.

What does -에서 do in 약국에서? Does it mean at or from?

-에서 can mean:

The place where an action happens (at/in).
The source/agent of an action (from), especially with institutions. Here it’s the source meaning: the service came from the pharmacy. This usage is common, as in 회사에서 연락이 왔어 (a call came from the company).

Why use 배달해 줬어 instead of just 배달했어?

V-아/어 주다 adds a benefactive nuance: someone did the action for someone’s benefit (often for me/us by default).

배달했어 = delivered (neutral statement of action)
배달해 줬어 = delivered for me/us, doing me a favor or as a service

How do I say this politely?

Change the ending to a polite level:

Polite informal: 배달해 줬어요.
Polite with subject honorific: 배달해 주셨어요.
Formal: 배달해 주었습니다 / 배달해 주셨습니다.

How do I show who received it or where it was delivered?

Add a recipient or destination:

Recipient (person): 나한테/저한테, 친구에게/친구한테, honorific –께
Example: 약국에서 나한테 약을 배달해 줬어.
Destination (place): 집에/집으로, 회사에/회사로
Example: 약국에서 우리 집으로 약을 배달해 줬어.

Is 약국에서 약을 배달해 줬어 active, and what’s the passive form?

Yes, it’s active (the pharmacy delivered it). Passive alternatives:

약이 배달됐어/배달되었어. (The medicine got delivered.)
Benefactive passive feeling (still focusing on me): 약을 배달받았어. (I received the delivery.)

Can I use 약국이 instead of 약국에서?

Yes:

약국이 약을 배달해 줬어 explicitly marks the pharmacy as the subject.
약국에서 약을 배달해 줬어 treats the pharmacy as the source/agent.
Both are natural; the -에서 version is very common in everyday speech when referring to institutions.

What’s the correct spacing: 배달해줬어 or 배달해 줬어?

Standard spacing separates the auxiliary 주다: 배달해 줬어.
You’ll see 배달해줬어 in texting, but 배달해 줬어 is the recommended form.
Also, 줬어 is the contraction of 주었어. Don’t confuse it with 주웠어 (from 줍다, picked up).

How is this pronounced naturally?

약국에서 is pronounced roughly [야꾸게서] due to consonant strengthening and liaison.
줬어 is [줘써].
So the whole sentence sounds like [야꾸게서 약을 배달해 줘써].

Can I drop the object particle -을 on 약을?

In casual speech, yes: 약국에서 약 배달해 줬어.
In careful or written Korean, keep -을: 약국에서 약을 배달해 줬어.

Can I change the word order?

Yes. Korean allows flexible order for non-verbal elements:

약국에서 약을 배달해 줬어 (most common)
약을 약국에서 배달해 줬어 (also fine)
Keep the verb at the end.

How do I make a question or a negative?

Yes/no question (casual): 배달해 줬어?
Polite question: 배달해 줬어요?
Negative (casual): 배달해 주지 않았어 or 배달 안 해 줬어.
Negative (polite): 배달해 주지 않았어요 or 배달 안 해 줬어요.

What’s the difference between 주다, 주시다, and 드리다 in this pattern?

V-아/어 주다: neutral benefactive (someone does something for someone).
V-아/어 주시다: honorific; the doer is respected. Example: 약국에서 배달해 주셨어요.
V-아/어 드리다: humble; the speaker (or in-group) does something for someone higher. Example: 제가 약을 배달해 드렸어요.

Could I say 로부터 or 부터 instead of 에서?

로부터/으로부터 is grammatical but formal/literary: 약국으로부터 (sounds stiff in speech).
부터 means starting point and isn’t used for agents here.
For natural conversation, stick with 약국에서.