Learn Hardcore Korean: naneun chinguege hangugeoreul gareuchigo chinguneun nahante yeongeoreul baewo. - I teach Korean to my friend, and my friend learns English from me.

에게 and 한테 both mark the indirect object (the person receiving the action). With 가르치다 (to teach), you teach to someone, so 친구에게 means “to a friend.” 한테 is more colloquial; 에게 is slightly more formal or written.

Why do we switch to 친구는 in the second clause instead of staying with 나는?

The topic/subject changes from 나 (I) to 친구 (friend) for the second action. By saying 친구는, you shift focus: “As for my friend, (he/she) learns English from me.” If you kept 나는, it would read “I teach and I learn,” which isn’t the intended mutual exchange.

Why is 나한테 used with 배우다, and can we use 나에게 instead?

Both 나한테 and 나에게 can mark the source (“from me”) with 배우다 (to learn). 한테 is casual; 에게 is more formal. So 친구는 나한테 영어를 배워 is friendly/plain speech, whereas 친구는 나에게 영어를 배워요 would be polite.

What role does the object particle 를 play in 한국어를 가르치고 and 영어를 배워?

를 marks the direct object—the thing being taught or learned.
• 한국어를 = “Korean (language)” is what is being taught.
• 영어를 = “English” is what is being learned.

What does the connective -고 do in 가르치고?

The verb ending -고 links two clauses, meaning “and” or “then.” Here it joins 가르치다 (teach) and 배우다 (learn) into one compound sentence: “I teach Korean, and my friend learns English.”

Why do both verbs (가르치다, 배우다) appear at the end, and what’s the overall sentence structure?

Korean is Subject–Object–Verb (SOV). Each clause places the verb last:
Clause 1: 나는 (subject) 친구에게 한국어를 (indirect + direct objects) 가르치고 (verb)
Clause 2: 친구는 (subject/topic) 나한테 영어를 (indirect + direct objects) 배워 (verb)

What level of formality and speech style is used here?

This is 반말 (informal/plain speech). The ending -어 in 배워 and the connective -고 are characteristic of casual conversation or writing among close friends.

Can the clause order or word order change without losing meaning?

Korean allows some flexibility, but verbs stay at the end of their clauses. You could swap clauses—친구는 나한테 영어를 배우고 나는 친구에게 한국어를 가르쳐—but it shifts emphasis and may sound less natural. The original order clearly presents “I teach first, then friend learns.”