Could following be a counter example to Church-Rosser (Confluence) theorem?
If we keep reducing the right subterm, then yes, we will never get to $v$. But noone says that we are restricted to this decision. The Church-Rosser theorem does not claim that any possible reduction series must lead to $N_3$. Church-Rosser just states that $N_2 \twoheadrightarrow_\beta N_3$, i.e. that there exists some beta reduction series that will lead from $N_2$ to $N_3$. And it is obvious that no matter how many times we just reduce back to $(\lambda u.v)((\lambda x.xx)(\lambda x.xx))$, at any point we can choose our next reduction step to be on the left-hand side, which will immediately get us to $v$. So it is possible to find a reduction series from both $N_1: v$ and $N_2: (\lambda u.v)((\lambda x.xx)(\lambda x.xx))$ to $N_3:v$ -- and that's all the Church-Rosser theorem states.