1. Given sufficient time and effort, sure she can.
2. I think he can cut her. Not as easily as wielder of vibranium knife did, though. It had some special effect on her.
Who'd win in a fight? It really, really depends on a person who writes it. There are at least a few instances where Emma in diamond form was shown to effortlessly use telepathy. Logan has many willpower and telepathy-resistance feats... it's hard to say.