CALM YOUR BEARD.
1. Wolverine: Origins, which is the - as of now - definitive backstory of Wolverine, shows that he had bone claws and that they, along with his mutant powers, manifested when he was trying to protect his father from being shot by his mother's drunk lover. The whole "lol, they're not ONLY made out of admantium" spiel happened in the normal Wolverine comics in Wolverine vol.2 #75, which came out in 1990-something, so if you haven't read Marvel since them days you're cruisin' for a shitload more of surprises. After Magneto did one of the most bastard things ever (re: ripping out all of the Adamantium in Wolverine's body all at once), during a training simulation some months later Wolverine basically collapses to the floor in IMMENSE PAIN when he unsheathes the bone claws through his
flesh.
Yeah, everyone else on the team WTF'D as much as comic book fans did.
2. His "Daughter" X-23, can't be part of the movie because she was cloned from him waaaaaay after his days in the Weapon X program, so sorry I had to burst your bubble like that. As to Wolverine looking like a girl: remember, this is a younger, 10-13 year old Wolverine who lived back in rural Canada sometime during the 1800s? He's a rich boy who never had to get his hands dirty, and the screenshot is admittedly grainy. ^_^
3. Wolverine is, to my knowledge, nowhere near an Omega-level mutant. Omega-levels are
much more powerful than Wolverine could ever be -- case in point: Iceman, Jean Grey, Vulcan, Franklin Richards, Storm, Gambit, Chamber, etc. He's described as being "another species" due to his female clone (and his own son) having different set-up for their claws, which would mark them for different "roles" in their society -- Wolverine is a warrior/hunter (three claws from each knuckle), X-23 is a breeder/home-maker (two claws in the first and last knuckle, and one claw from somewhere in her foot), and Daken (his son), would presumably be a gatherer? I guess? (two from the first and last knuckle, and one claw from the place where spider-man shoots his webbing.) It sounds like bullshit, I know, but that's comics for you.
4. In all of its iterations, the Weapon X Project is headed by Department K, which is a Canadian paramilitary group funded by SHIELD and the United States. If the movie takes place DURING Wolverine's stay at the Weapon X facility, it would make sense that Deadpool wouldn't have his face fucked up, because Deadpool's cancer didn't go apeshit all over his body until the program implanted a faulty regeneration factor inside of him. I'm also going to have disagree on you with the whole "Wolverine would have no offensive capabilities" thing, because before his Weapon X days Wolverine worked with Captain America to kick some Nazi butt on missions normal people wouldn't
dream of volunteering for.
5. Wolverine's Claws, from Wolverine: Origin (it looks like they're including this scene in the movie to explain his backstory.)
6. His biological son, Daken. (note the bone claws)
7. x-23, his cloned "Daughter". (again, boney claws).