I don't think it sounds advanced at all. Just scatter-brained, if anything.

Which I'm guilty of from time to time.
I don't know anything about Trigun, except that I've seen two music video collaboration blurbs, in which Vash danced to "The Safety Dance" and the guy with the Star of David sang "Pretty Fly for a Rabbi".
BUT... Let me say this much in the new character matter. One, I'd prefer you just keep Jack young and NOT have him be a martial arts god than age him. My main reason for this, as Blaze stated, is that he's been 17 for the whole thread, and hasn't yet done anything too extraordinary. Having him become comparable to the version of Chuck Norris that all the jokes refer to would be changing his character, as would making him older. All of my old instructors, who were world champions in their own right, had only really mastered one form of karate, and the one who did more than one had only done a few others. To have trained intensely in each of those forms would be nigh impossible, and altogether ineffective against Vampires at the end of the day. You break his neck, he snaps yours back with a lop-sided head. You smash his temple, he bear-hugs you. You do anything the heck you want to him short of knocking his head clean off or tearing his heart out his ribcage and your karate training all goes down the crapper.
Jack doesn't need any more changing. He just needs to do what he can and work with everyone. Holy implements will be your best weapon, rather than sword or fist.
One more thing I want to touch on... between mentions of Hellsing(which, admittedly, Drama and I were inspired by too) and Trigun, coupled with the whole jumping down from the roof of a big building makes me a bit concerned. Despite the presence of Vampires and the like, a touch of realism in our human characters is something we're all going for. This is my big pet peeve with anime; people watch it, fall in love with the unrealistic and powerful characters, and then incorporate such attitudes, characteristics, and fighting styles/weapons into their own characters. Brother Nicodemus and Van Adruian, for example, borrow nuances from Alucard and Anderson, but could stand on their own without any basis on them; they're just fanatics, one of them very old-world, and another more adapted, both grim, one more outwardly tortured by his plight, not overly proud or masculine, humble, obedient, the kind of stuff you don't see in Alucard or Anderson.
Anime rant aside, please stick with Jack and try and work out a way for him to fit the situation. Because no matter how good he gets in most fighting styles, you don't fight the Undead like you do a human. Jack's ability to pray and knowledge of how to whip out the right holy weapon will benefit him a lot more than knowing how to put a vampire on its back with a broken face, neck, and large intestine.

And as for Hatiyai, its best if she make up her own character. I have to run Van Adruian for Drama, and trust me, its not fun having to worry about keeping someone true to another person's character. A little bit of planning will go a very long way here. She CAN take a premade character, but I discourage it.