a) as I said previously, I don't think it makes sense to ask about the degree of a function R^2 -> R^2
b) since f maps 0 -> 0 and R^2 -0 -> R^2 - 0, it makes sense to ask about its local degree at 0 and f restricts to a map S^1 -> S^1, which has that degree by comparing the defns
c) yeah, degree 2 sounds about right for that