For the first part, I believe it is just tracing, right? I look at the line at (0,1) and then follow it, but it's a little confusing.

It says how many critical points...well a critical point is when it is undefined or has slope zero. It seems like there is a whole line of critical points of slope undefined (i.e. the vertical lines) and a few lines that are horizontal..i.e. slope that correct or are there not that many?

I don't know what they mean by what types? I assume just slope=0 or undefined? I got the relation as y=10/x^2.