The home page of the Polish Virtual Library has a good search interface and the older issues of the classical Polish journals such as Fund. Math., Studia Math., etc. as well as the monograph series are available for free more or less in their entirety. Here's a link to the old repository which is...

Question 2: As Mariano points out, we can lift $\Phi \in \operatorname{Diff}^+{(\mathbb S^1)}$ uniquely to a diffeomorphism $\phi : \mathbb{R} \to \mathbb{R}$ such that $\phi(0) \in [0,1)$ and $\phi(x+1) = \phi(x) + 1$ for all $x \in \mathbb{R}$. Lift $\Psi$ similarly to $\psi$. For $t \in [0,1]...