Is $\frac{0}{\infty}$ indeterminate? I have been searching for an answer for this for half an hour and I can't seem to find one. I've lots of information about other combinations of $0$ and $\infty$ but I haven't seen anything that says whether $\frac{0}{\infty}$ is indeterminate?
This quotient is zero. This is true whether you mean projective infinity or extended positive infinity.

Since you say "indeterminate", I assume you're talking about limit forms. Well, division is continuous and defined at $0/\infty$, so this is, indeed, not an indeterminate form.

This is actually pretty easy to show that this limit form works out to $0$ by the $\epsilon-\delta$ definition of limit: you should try to do so on your own. (and ask a new question here on MSE about it if you get stuck)
$$[\frac{0}{\infty}] = [0 \cdot \frac{1}{\infty}] = [0 \cdot 0]= 0$$

so it isn't.