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

Questions: In dimension $n\geq 5$,

1. is it possible for a manifold to be homeomorphic to an open subset of $\mathbb{R}^n$ but not diffeomorphic to it?

2. is it possible that two homeomorphic open subsets of $\mathbb{R}^n$ may be non-diffeomorphic?

(the smooth structure on each open subset of $\mathbb{R}^n$ being the standard one).