Up to dimension 3, homeomorphic manifolds are diffeomorphic (in particular, homeomorphic open subsets of $R^n$ ($n\leq 3$) are diffeomorphic). It is known that there are uncountably many mutually non-diffeomorphic open subsets of $R^4$ that are homeomorphic to $R^4$ (Demichelis & Freedman - 1992). For $n\neq 4$, $R^n$ admits a unique differential structure, thus the previously mentioned phenomenon is unique to dimension 4.

Question: In dimension $n\geq 5$,

(1) is it possible for a manifold to be homeomorphic to an open subset of $R^n$ but not diffeomorphic to it?

(2) is it possible that two homeomorphic open subsets of $R^n$ may be non-diffeomorphic?