Question on dynamic of $y'(t)=\sin(y(t))$ and on nature of equilibrium point of $y’=|\sin(y)|$.

Let $ y’=\sin(y)$ an ODE. I just try to imagine the dynamic behind.

Q1) First, on $ \mathbb R$ we only have $ \mathcal C^1$ piecwise solution, no ? Because, when for example $ y(t_0)\in (0,\pi/2)$ , then, $ y(t)\to \pi/2$ , and when the particle will arrive in $ \pi/2$ , then it will sotp and never go again. And so, I can’t get a smooth solution on $ \mathbb R$ . Am I right ?

Q2) Now, if $ y’=|\sin(y)|$ , what will be the nature of $ y=\pi$ ? Because it’s an equilibrium point, but it will be stable at left and unstable at right. Can I call it a saddle ?