I would like to better understand the relationship between different notions of orientable sphere bundle. Let me say that a locally trivial fiber bundle $\pi\colon E\to M$ with fiber $S^n$ and structure group $G$ is a 

topological sphere bundle if $G=\mathrm{Homeo}^+(S^n)$,

smooth sphere bundle if $G=\mathrm{Diffeo}^+(S^n)$,

linear sphere bundle if $G=\mathrm{Gl}^+(n,\mathbb{R})$.

It is known that there exist smooth sphere bundles that are not equivalent (as smooth sphere bundles) to linear sphere bundles (see e.g. the following posts here on MO):

https://mathoverflow.net/questions/116003/examples-of-sphere-bundles

https://mathoverflow.net/questions/74756/is-it-true-that-all-sphere-bundles-are-boundaries-of-disk-bundles

For example, in an answer to the second question linked above R. Budney shows that there are smooth sphere bundles over $S^2$ which are not linear. Here comes my first question:

1. Is it possible to construct a smooth sphere bundle over $S^1$ which is not smoothly equivalent to a linear one? One could take an exotic diffeomorphism  $f\colon S^n\to S^n$, and consider the mapping cone of $f$, which is a smooth sphere bundle. Is this bundle linear? 

The second question is about topological bundles:

2. Do there exist a topological sphere bundle which is not topologically isomorphic to a linear one (or even to a smooth one)?