We can reuse old features and market them as new. Wouldn't make it any good, though. Just because you can do something doesn't mean you should.
Some classes are remarkably similar, not all. And that is because they have to follow certain rules (so, shockingly, a new class would fill roles that previous ones did). That's hardly a reason to throw a new garment at an existing class and call it a new one.
No, you can't change what they do. You can only change how it looks with class skins.
In the realm of feasibility. There's no reason for Tinkers to perma-stealth while wearing a claw pack (cat form) as you suggested. You just throw in whatever you think is cool instead of what is suitable.
Because you already have the Tank and the DPS aspects.
Check up on Gazlowe and Mekkatorque to get an idea of what a Tinker is.
Monks would like to have a word with you
Damn... you're clueless.
And how would it differ beside doing the same things a Death Knight does, just from range?
While in Robo-form?
And that is still highly unlikely, because stealth isn't usually part of the Tinker fantasy.
If you'd check out lore, you'd see the class is mostly associated with them, since they are the only technological races (other than the Dwarves, and of course the Mechagnomes).
Do you realize it doesn't require mounted combat?
It would be like a Demon Hunter's Metamorphosis.