So I have some questions about singularities that should be rather simple to clear up. First of all, is a zero of a function a removable singularity? So if I have f(z)=$e^{z}-1$ is z=0 a removable singularity?

Can a function have multiple singularities? (I assume yes but since we're here we might as well be safe)

Now say I have something like $sin(1/z)$. When $z=0$ what type of singularity do we have? Do we have a pole (1/z clearly goes to $\infty$)? Do we have a removable singularity (the sin is bounded between 1 and -1)? Or is it essential (if it were to be neither since sin can be rewritten with the Euler formulas and isn't bounded by Liouville's theorem)