I understand what you are saying. But you are forgetting that she is not an adult. She is a kid and kids sulk when you take away their privileges or snip their wings. You can't expect her to act "normal" after you have taken away her computer, even if she did sneak onto it instead of finishing her homework.
That doesn't mean you don't hold her feet to the fire. Work first, then "x" amount of time on the computer, "x" amount of time with family, etc.
As to the manga convention, YES, let her go. If she were interested in ballet, or drawing still life pictures, or basketball, you would be happy about that. Drawing manga is just as complicated as drawing anything else. And writing graphic novel stories is a great way for her to learn creative writing.
There are lots of people who host foreign exchange students and many families whose kids become exchange students. You have no idea how much you as a family could get out of that, including opening your families and daughter's minds to different cultures, and learning all kinds of wonderful things. I realize you might not want to do it, but I really think that you don't realize how much you are squashing your daughter's interests by just flat out saying no to her without even pretending to look into it. She is interested in another culture, and she feels like you hate that about HER.
You aren't an "evil" mother, but you are shortsighted thinking that she did something wrong and didn't "fix" it, but made it worse by crying and asking for some kind of support from you for her dream. I cannot imagine that you haven't done the same kind of thing as an adult (without the tears) in trying to REFRAME the conversation when you feel someone else is not listening to you.
Remember that she is not an adult. You might win the battle, but lose the war. At some point when she is older, she might not even try to get your approval for what she is passionate about, and she might find something else to like that is totally inappropriate. You would both be better served by working together to foster this interest of hers. Tell her what you expect from her, and then give her a carrot. If you are only using a stick, she has NO incentive to work with you. She knows you can't keep the computer away from her forever, and if you are TOO strict, she will just find some way to sneak around. Instead, co-opt her into doing the right thing because she decides to do it. Working together, her giving, you giving. It will really help you both a lot as she goes into her older teen years.
Good luck,
Dawn