For a) you're right although maybe it would be more appropiate to write in case you decided to let . For b) you need to verify whether there exists a linear transformation such that . For c) you're right.
Hint:Spoiler:
Kind of, it will give you that the function can't be differentiable if , but to prove differentiablity in case n>1 you'll need the definition I gave you. Before looking at the hint, notice that in case n>1 the function approaches zero very fast near the origin (try to picture it in one dimension) so the derivative must be...
Hint:Spoiler: