I haven't watched the entire 07 Ghost anime but I'll try my best to help you with your character.
First, it might be a good idea to eliminate her position as Teito's sister. It's generally considered a cop out idea to just add a character in as XXX's relative. Unless Teito having a sister he doesn't know about is extremely plausible within canon (meaning that in the series there are reasons why Teito would have an unknown sister) than you shouldn't make them related. The only fanfiction I've read where the added on brother/sister thing really worked was one where the writer had pretty much reversed the original premise and made an almost seperate world. Since I don't think you want to do that it may be a good idea to have your character as someone who is from the Raggs kingdom and wants to restore its power. She could potentially see Teito as a role model for her goals.
Secondly, a good original character has flaws. What makes a Mary Sue is that she's perfect. Your character can't be good at everything. She needs to not just have flaws related to things like cooking but personality flaws as well. For example, she could be rash or insecure. Whatever the flaw, these need to become a problem for her later on. For example, if she is headstrong than you can't have every stupid decision she makes turn out well for her. There need to be consequences, good or bad, for her actions that will allow her to change and develop as a character. 'Change' is actually the markings of a good character: if you allow her to grow personally than she will automatically become more realistic.
Thirdly, I do believe that your decision to put her into the Black Hawks is Mary Sue-ish. From what I know, these special groups, such as the Akatsuki or the Black Hawks, are extremely exclusive. Only the best of the best would be put in there. Miroku would not just put someone in that group because it would be interesting or so he could keep an eye on her. He wants that group to be elite and wouldn't allow someone will low caliber skills into the group. There are many more positions you could put her in where she could be watched. Now, getting into the Black Hawks could be a goal she has. To make this goal plausible then you need to have her work for it. Just like she needs to change personally to reach her goals she needs to change physically as well.
Lastly, personalities are important. Your character's personality seems to clash with her goals. With some good planning this could become a springboard for character development: she needs to become stronger to attain her goals. However, she can't automatically worm her way into everyone's hearts with her personality as it is. The main thing you never do in an original character fanfic is bend every canon character's personality to interact in some way with your character. A good original character will blend into the world very well. For example, if Ayanami would coldy brush her off than have him do that. If you want her to interact with characters in a certain way then you need to have her learn to act a certain way. While trying to make relationships with canon characters you could have her worming her way into a character's heart as well. There's nothing wrong with developing friendships or romances between canon and original characters, you just need to make it believable.
As for her abilities, you need to consider the setting you are putting her in. If a healing ability wouldn't work very well than give her another ability. If you want her to have healing than you should give some good reasons as to why she was allowed into the military with that power. Giving her two zaiphons is probably better to stay away from: even if the idea is explored in canon it would come off as Mary Sue-ish. Find an ability that would suit her personality and would help her attain her goals. If you do this than your character will seem more realistic.
Just remember this: if your character acts like a real person than you will have a good original character.