뭐하니/뭐하냐 What are you doing? People in regional provinces rarely use -니 since it sounds goody-goody. They use -냐 more often, so do I. I might use -니 when I'm upset(like "너 같으면 기분 좋겠니?") or I talk to a little kid.
-잖아 is used to inform someone of something they're not aware of although they are supposed to be.
나 자고 있었어. I was sleeping.
나 자고 있었잖아. I was sleeping, wasn't I? (imlplies something like "Why did you wake me up?" or "So I didn't know you came in" etc, depending on the situation)
Also, you can use -잖아 when you're upset.
A : (watching TV)
B : (stands before A, so A can't watch TV)
A : 야, 비켜. 안 보이잖아. Hey, move over. I can't watch TV(Why are you standing there?).
안 보여 would be a nicer say of speaking, but if you're close friends, none of you will take offense at it. Though you could be screwed if your friend had a bad day.
A₁: 그 강아지 귀여워요? Is the puppy cute?
B₁: 아뇨. No.
A₂: 그 강아지 귀엽죠? Is the puppy cute, isn't?
(I think the puppy is cute and I'm sort of sure you think so.)
B₂: 아뇨. No.
A₂will be more disappointed.
In assertive sentences, 죠/지(요) implies your attitude toward what you say.
A : 안 졸려? Aren't you sleepy?
B₁: 졸려. I am.
B₂: 졸리지. I am. (and it's natural for me to feel sleepy)