Answer
See the detailed answer below.
Work Step by Step
$$\color{blue}{\bf [a]}$$
See the graph below.
$$\color{blue}{\bf [b]}$$
At $n=2$, we can see from the graphs below that the probability of finding the particle at the center of the well is zero since $|\psi(x)|^2=0$ there.
$$\color{blue}{\bf [c]}$$
Yes, this is consistent with what we know about standing waves. In the $n=2$ state, the wave function has 3 nodes, one of which is just in the middle.
