For the questions, I have used the equation: $E_{kin}=\frac12\times m\times v^2$, $m_e=9.11\times10^{-31}$ kg.
When I plugged in the given numbers, I got my answer but my online homework keeps marking me down. I do not understand what I did wrong. $\frac12\times(9.11\cdot10^{-31})\times(6.12\cdot10^{14})$.
$h\nu = \phi + E_k$
where $\phi$ is the work function of cesium ("escape energy" - think of it as analogous to the energy required for gravitational escape from a planet, if you're more familiar with that) and $E_k$ is the kinetic energy. $h$ is the Planck constant, $\nu$ is the incident photon frequency.
So $E_k = 6.626 \times 10^{-34} \times 6.12 \times 10^{14} - 3.364 \times 10^{-19}$. The last number is the work function of cesium in joule (most give it in electron-volt, it's an easy conversion). The result is $E_k = 6.911 \times 10^{-20} \mathrm{J}$.
From that, you can work out the velocity of the proton. Using $E_k = \frac 12m_pv^2$ (where $m_p$ is proton rest mass), you get $v \approx 9091 \mathrm{m/s}$. You have to be a bit careful in this step. If your speed were to have come out close to the speed of light, you need to ignore the results of this calculation and use the special relativistic formula $\displaystyle E_k = (\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}-1)m_pc^2$ to solve for $v$ correctly. In this case, the approximate Newtonian formula is fine.
My post is meant mainly as a guide - you should redo the calculations using the values of constants you're supposed to use with attention to the correct number of significant figures, etc.