I've said in the past I think this could be fixed by adding a new fighting style for Direct The Strike and a couple of maneuvers including one that makes someone spend hit dice.
Aberrant Mind Sorcerer hits almost every single point of a sorcerer. Uses power points (fully interchangeable between metamagic and spells) and has all the psionic abilities/spells including getting to use them like psionics.
The swordmage is very different from the other two. Delivering a spell through a sword should, I agree, be a thing - but it's starting to drift into the territory of the Paladin smite spells (with the Paladin having expanded massively thematically and pressuring Gish classes because of it)
Agreed
Storm Herald Barbarian has Tundra as one of the choices and Circle of the Land Druids get arctic as a choice. There should however be both clerics and sorcerers of winter.
Bards certainly have unique spells. I don't think they have many but they definitely have Vicious Mockery as a cantrip and Dissonant Whispers at first level. (Note: this does not include subclass poaching). Possibly unique spells for subclasses would be an idea.
Both Ranger and Paladin qualify here.