Seems like Rogue doesn’t have Ms. Marvel’s powers but we don’t know anything for certain until we see the extent of Rogue’s powers after Messiah Complex. She hasn’t had her powers for quite some time now.
Wolverine was a Mutant before he got the adamantium in his body. You have to be born a Mutant, with your powers showing up either at birth or during puberty but this varies. People who got their powers in any other way (Hulk, Spider-Man, etc) are not Mutants. It has to be in your DNA, like having black hair and brown eyes and so on.
Wolverine’s healing factor was his original Mutant power but it was revealed years later that he also had claws made out of bones. Along with keen animal senses, advanced hearing, able to track people by scent, etc. His powers manifested during puberty.
Lady Deathstrike isn’t a Mutant in Marvel comics, only in the second live action X-Men movie is she a Mutant. Her body has been fixed up to house Adamantium. Long story, the 90s X-Men cartoon can give you the cliff notes on it. Just ignore the part about Deathstrike and Wolverine being lovers in the cartoon and there you go.
The reason why Lady Deathstrike can handle Adamantium (if it’s in your bloodstream and you don’t have a healing factor, it will kill you which is why Sabretooth and X-23 can handle it) is because of enhancements made by Spiral in the Mojoverse and her Body Shoppe, using technology that is more advanced than ours, including some magic too.
X-23’s a clone of Wolverine so that’s why she has a healing factor and can handle Adamantium.
Sabretooth has had Adamantium twice. It was removed once but then a new Weapon X facility/army/project/ongoing comic/whatever you want to call it gave him an Adamantium skeleton again. In his latest appearances in Wolverine and X-Men, Sabretooth didn’t have an Adamantium skeleton and this has not been explained yet. Well Sabretooth is currently dead right now so this just may go on as an unanswered question.
Jeph Loeb was asked directly over at Newsarama why does Sabretooth not have his Adamantium (among other things in his Wolverine run) and all he said was something to the effect of “Romolus is sure messing with those feral Mutants, isn’t he?” So I suppose that’s the only explanation we have. You probably don’t need to know anything about Romolus (please don’t ask, I for one do not want to revisit this horrible storyline lol) just that he was a bad guy that pulled a lot of strings to do a lot of evil crap, you know like Mystique did in Messiah Complex. 