What Am I Riddles

Question: A thousand wheels, but move I do not.
Call me what I am, call me a lot.

What am I?

Question: Soft and cuddly, I'll pull on your heart.
But take my last name and I'll tear you apart.

What am I?

Question: I drape the hills in white,
I do not swallow, but I do bite.

What am I?

Question: I used to fill rooms but now I'm a tower,
I can stay put or I can travel far.

What am I?

Question: My first doth affliction denote,
which my second is destined to feel.
And my whole is the best antidote,
that affliction to soften and heal.

What am I?