1.) $1$

2.) Does not exist, since $\log(0)$ is undefined.

3.) $\pi$

4.) $1$

5.) Nothing. Knowing those two limits tells you nothing about the one in two variables -- it does not exist.

6.) It is continuous everywhere except on the line $y = e^{\frac{x}{2}}$.

7.) It is continuous everywhere except for where $y < 0$. Another way to say this is that it is "continuous on the upper half-plane" (including the $x$-axis).

8.) $1$

9.) Does not exist. Approaching $(0,0)$ along the line $y=x$, you get a limit of $\frac{1}{2}$ but along the line $y=2x$ you get a limit of $\frac{1}{5}$.