잘지내십니까? correct! very formal. 잘지내시니요 -> 잘지내시지요? very formal. 잘지내요? correct! between formal and casual. 잘지내? casual. 뭐해? casual. same means "What are you doing? 요즘 어때요? formal and casual. same means "How are you?" 요즘 어때? casual. same above. hope you helps.

You are correct. You could also say: 어떻게 잘 지냈어요? Literally "how have you been?". You can still reply with 잘 지냈어요 but I find people will usually tell u how they have been if you ask this way (but I believe its only appropriate with people u have met before or know well). U could always ask 요즘 바빠요? You busy these days? I hope this helps :)

Hi. I'd like to take some examples for you. 1. If you meet somebody almost everyday, Just saying '안녕하세요?' is enough. 2. If you meet somebody sometimes, 잘 지냈어? (Casual) 잘 지내셨어요? (Formal) 3. If you write a letter or send a text message to someone who you haven't met for a while, You can start the sentence with 잘 지내? (Let's say i was broke up 3 month ago, and my ex-boy friend wants to get in touch with me again, he would send a message that starts with ' 잘 지내?'. ㅋㅋㅋ(ㅋㅋㅋ means lol in korean shortened online expression) 도움이 되었길 바래요 :)