Learn Hardcore Korean: chinguege sukjereul dowadallago butakhaesseoyo. - I asked a friend to help me with my homework.

The structure breaks down into three parts:
• Verb stem + 아/어: e.g. 돕 → 도와
• 달라고: “asking someone to give you that action” (from verb 달다, “to give”) plus the indirect‐speech marker -고
• 부탁하다: “to request a favor”

So 도와달라고 부탁했어요 literally means “I requested (them) to give me help”—in natural English, “I asked (my friend) to help me.”

Why is 친구에게 used instead of 친구를?

에게 marks the indirect object or the target of an action—in this case, the person you are directing your request to (“to my friend”). Using 친구를 would mark “friend” as the direct object of a verb, which doesn’t fit here because you’re not doing something to your friend but asking them to do something.

Can I use 친구한테 instead of 친구에게? What’s the difference?

Yes. 친구에게 and 친구한테 both mark “to my friend.”
• 에게 is more formal or written.
• 한테 is colloquial and used in everyday speech.
Both are correct; choose 한테 in casual conversation and 에게 in more formal contexts.

Why is 숙제 marked with -를, as in 숙제를?

Because 숙제 is the direct object of the verb 도와 달라다 (“to help [someone] with something”). The object marker -를 tells you that “homework” is what is being helped with.

How would you say the same idea in present tense?

Change the main verb 부탁했어요 (past polite) to 부탁해요 (present polite):
친구에게 숙제를 도와달라고 부탁해요.
This means “I ask my friend to help me with my homework.”

What’s the difference between reporting this request (도와달라고 부탁했어요) and directly asking your friend to help you?

• Direct request (to your friend): you’d say 숙제를 도와주세요 (“Please help me with my homework”) or 숙제 도와줄래요? (“Would you help me with homework?”).
• Reported request (to someone else): you use the indirect‐speech form 도와달라고 부탁했어요, which says “I asked them to help me.”

How can this sentence be made more formal or polite, for example in a business setting?

Use the honorific form 부탁드립니다 and the honorific auxiliary 주시다. For instance:
친구(분)에게 숙제를 도와달라고 부탁드렸습니다.
This raises the politeness level and shows respect toward the person you asked.

Why isn’t there an explicit subject like “I” or “me” when talking about who receives the help?

In Korean, the beneficiary (“me”) is understood from -아/어 달라고—it inherently means “do something for me.” The speaker doesn’t need to say 저에게 or 나에게 because it’s already implied that the request is on the speaker’s behalf.