They are mostly correct, but one thing to note is that -아/어/여도 돼요? sounds like asking for permission. So it is a good phrase for "Is it okay to ...?", but not the best one for "Do/Would you mind if I ...?". For the latter, -도 괜찮겠어요/괜찮을까요? or -도 될까요? would be better. 1. Is it okay if I use my phone while I wait? = 기다리는 동안 휴대폰을 써도 돼요? OK 2. Do you mind if I read out loud? = 제가 소리내어 읽어도 쾐찮아요? OK, but 괜찮겠어요? would be more polite. 3. Do you mind if I go first? I have to take an exam right now. = 저 먼저 가도 쾐찮아요? 지금 당장 시험을 봐도 돼요. (The second part is wrong) => 저 먼저 가도 괜찮을까요? 곧 시험을 봐야 해서요 / 봐야 돼서요. (시험을 봐도 되다 = its is okay to take a test. 시험을 봐야 되다 = I have to take a test) 4. Teacher, could you explain this to me? I didn't understand this topic well. = 선생님, 이걸 설명해 주실래요? 이 주제를 잘 알아들을 수 없었어요. => 선생님, 이거 (다시) 설명해 주시겠어요? 잘 이해가 안 돼서요. (주실래요 sounds too casual to a teacher) 5. Do you mind if I bring my puppy with me? I don't want to leave it alone. = 저와 강아지를 거져와도 되요? 내버려두고 싶지 않아요. (저와 and 가져와도 don't sound right. 가져오다 is for things. For pets, 데리고 오다/데려오다 is better) => (제/저의) 강아지를 데리고 와도 될까요/괜찮겠어요? 혼자 두면 안될 것 같아서요 / 혼자 두고 싶지 않아서요. -아/어/여서요 is a common phrase for giving a reason for what was just said.