sukjereul haeseo chinguwa norayo.

-아서/어서 is a connective ending that links two verbs. It can express:

• Sequence (“do A and then do B”) as in 숙제를 해서 친구와 놀아요 (“I finish homework and then play with my friend”).
• Reason or cause (“because A, B happens”), e.g. 배가 고파서 밥을 먹었어요 (“I was hungry, so I ate”).

Here, it shows you complete the first action before moving on to the second.

Both -아서/어서 and -고 connect actions, but:

• -고 is a neutral listing connector: “A and B” without implying cause or sequence strongly.
  Example: 책을 읽고 텔레비전을 봐요 (“I read a book and watch TV”).
• -아서/어서 emphasizes that A is a prerequisite or direct cause/sequence of B.
  In 숙제를 해서 친구와 놀아요, doing homework is necessary before playing.

Both -와/과 and -랑/이랑 mean “with,” but differ in formality:

• -와/과 is slightly more formal or written.
• -랑/이랑 is colloquial and very common in speech.

You can say 숙제를 해서 친구랑 놀아요 in everyday conversation without changing the meaning.

Korean often omits the subject when it’s clear from context. The listener infers that I (저 or 나) is the subject. Including it is possible but usually unnecessary:

• (저가) 숙제를 해서 친구와 놀아요
  This is correct but more formal or emphatic.

놀다 (“to play”) is a verb ending in a vowel stem (ㄹ). In the polite present tense:

• Drop 다 → 놀-
• Add -아요 → 놀아요
  This is the standard polite style you’ll use with strangers or acquaintances.

-를/을 marks the direct object of a verb. Since 숙제 (“homework”) is what you’re doing:

• Vowel-ending noun + -를 → 숙제
  • -를 = 숙제를
    This tells us “homework” is the thing being done.

Yes. Change both verbs to past polite forms:

• 하다 → 했어요
• 놀다 → 놀았어요
  So you get: 숙제를 해서 친구와 놀았어요 (“I did my homework and played with my friend”).